Obama, though, was unable or unwilling to rhetorically underscore the severity of the crisis as it unfolded, so perhaps what should have been seen as successes were seen as failures. “It was a delicate balance throughout 2009 and 2010 to be straight with the American people about the depths of the problem, how close we were to disaster, without scaring the heck out of them,” Obama said.

Beyond the messaging challenge, Obama faced a practical bind as well: Just as he was trying to reinflate the economy, he was also being forced to cut government jobs, under pressure from Republicans who contended that government bloat and the cost of it could create our next financial crisis. Call it an anti-stimulus. “This is the first recovery where you actually saw the government work force decline, and that created this massive fiscal drag throughout the recovery,” Obama said.

Despite all this, over the course of his presidency, Obama has actually been able to oversee a much larger stimulus than has been typically reported. If you add up all of his administration’s classic stimulus measures, including the many tax breaks the administration extended, you get $1.4 trillion, a figure that is nearly twice the original figure. The anti-stimulus, then, was counteracted by a stealth stimulus.

“Progressives don’t fully appreciate the degree to which the 2011 budget deal not only averted a potential default but actually limited the potential damage of a newly emboldened Congress in imposing austerity on a still-fragile recovery,” Obama said. “And by me winning in 2012 and getting the Bush tax cuts for the upper 2 percent repealed, we ended up getting a grand bargain. It’s just we got it sequentially instead of all at once.”

When I asked Barney Frank about how history will judge the recovery, he was simultaneously rueful and amused. As chairman of the House Financial Services Committee, Frank was one of the major legislative architects of Obama’s economic program. “You get no credit for disaster averted or damage minimized,” Frank said. By way of illustration, he described a bumper sticker that a friend made him in 2010, with a slogan that could have worked just as well for Obama: “Things would have sucked worse without me.” Frank, with a halfhearted laugh, added, “That’s not a very salable message.”

Often in our conversations, the president expressed a surprising degree of identification with America’s business leaders. “If I hadn’t gone into politics and public service,” Obama told me, “the challenges of creating a business and growing a business and making it work would probably be the thing that was most interesting to me.” His showy embrace of capitalism was especially notable given his fractious relationship with Wall Street and the business community for much of his first term.

In December 2009, Obama was not reluctant to chastise bankers. “I did not run for office to be helping out a bunch of fat-cat bankers on Wall Street,” he told Steve Kroft on “60 Minutes.” “The people on Wall Street still don’t get it. They don’t get it. They’re still puzzled, ‘Why is it that people are mad at the banks?’ ”

Given the national mood at the time, Obama’s words shouldn’t have come as a surprise to the business leaders. But the financial sector had buoyed Obama’s campaign, giving him $16 million in political support, nearly twice what McCain received from it, and some executives responded to his new populism in emotional terms. “It’s a war,” Stephen Schwarzman, a co-founder of Blackstone Group, the giant private-equity firm, said of Obama in 2010 and his effort to close a tax loophole that benefited the industry. “It’s like when Hitler invaded Poland in 1939.” (Schwarzman later apologized.) Others seemed more concerned with the language itself. In 2011, Leon Cooperman, a billionaire hedge-fund manager, wrote a public letter to Obama, saying: “The divisive, polarizing tone of your rhetoric is cleaving a widening gulf, at this point as much visceral as philosophical, between the downtrodden and those best positioned to help them. It is a gulf that is at once counterproductive and freighted with dangerous historical precedents.”

When I asked him about these reactions, Obama laughed. The criticism he leveled at Wall Street “was extraordinarily mild,” he said, but “it hurt their feelings. I would have some of them say to me, ‘You know, my son came home and asked me, ‘Am I a fat cat?’ ” He laughed again.

Obama’s rhetoric does seem mild, at least compared with the withering contempt of, say, Franklin Roosevelt, who, laying out the objectives for the second stage of the New Deal in 1936, said that reckless bankers and speculators are “unanimous in their hate for me — and I welcome their hatred.” Obama, to the contrary, seems to find their hatred irritating. “One of the constants that I’ve had to deal with over the last few years is folks on Wall Street complaining even as the stock market went from in the 6,000s to 16,000 or 17,000,” he said. “They’d be constantly complaining about our economic policies. That’s not rooted in anything they’re experiencing; it has to do with ideology and their aggravations about higher taxes.”

Wall Street’s biggest fight with Obama was over the Dodd-Frank Wall Street Reform and Consumer Protection Act, which Obama signed into law in the summer of 2010. The legislation, which runs to 2,223 pages, limited Wall Street’s riskiest trading schemes, established the Consumer Financial Protection Bureau and created a system to wind down failing banks without taxpayer-funded bailouts and break up banks that don’t comply. Like the stimulus, Dodd-Frank has been seen as both going too far and not far enough.

Some economists have suggested that the reform package, combined with the Federal Reserve’s efforts to force the banks to hold more capital, most likely slowed lending and potentially economic growth in the short term. The new rules may have been sensible in the aftermath of the crisis, but they did take an economic toll. “Growth requires access to capital to finance investments in plant, equipment, technology, and workers,” said Douglas Holtz-Eakin, a former director of the Congressional Budget Office who now runs American Action Forum, a right-leaning research group. “Dodd-Frank made capital scarcer and more expensive at a time when the weak economy desperately needed a boost to growth.” Holtz-Eakin estimated in 2015 that the regulations would shave $895 billion off gross domestic product over the next decade.

Obama sees the legislation in more complicated terms. He said that he liked the film “The Big Short” — a vivid portrayal of the 2008 crisis with a special emphasis on the avarice of its main architects — but not its ending. It suggests, wrongly, he said, that nothing has changed on Wall Street. The financial sector “is bigger, absorbs more resources and maybe most importantly, more talent than I would like to see. I would like folks who are really good at math to be going into engineering and the sciences more than they’re going into trying to build algorithms to beat the market and to work arbitrage,” he said.

“But there is no doubt that the financial system is substantially more stable,” he said. “It is true that we have not dismantled the financial system, and in that sense, Bernie Sanders’s critique is correct” — a reference to the Vermont senator and presidential aspirant who regularly calls to break up America’s biggest banks. “But one of the things that I’ve consistently tried to remind myself during the course of my presidency is that the economy is not an abstraction. It’s not something that you can just redesign and break up and put back together again without consequences.”

The Saft America plant, a giant 235,000-square-foot mass of concrete, is a modern marvel: its roof covered in row upon row of solar panels, embodying the renewable future that the batteries manufactured within are meant to sustain. (The main customer for the batteries was originally meant to be electric-car manufacturers, but the company is now selling mostly to utilities who want to store solar and wind energy.) Obama spoke from a makeshift stage set up at the center of the factory floor, an American flag and a Saft logo perfectly positioned behind him to catch the sight lines of the photographers.

“The reason I’m here today is because Saft is telling a story about the amazing work that people all across this country have done to bring America back from one of the worst financial crises in our history,” Obama said, surveying the crowd.

He added: “Anybody who says we are not absolutely better off today than we were just seven years ago, they’re not leveling with you. They’re not telling the truth.”

The story Obama told was one of American ingenuity and growth since the financial crisis. Unemployment in Florida peaked at 11.2 percent in 2009, higher than the national average, and the state was a center for home foreclosures. Saft America was an example not of the government’s effort just to reduce unemployment right now, which it has, but also to spur investment in the next-generation green technologies, like lithium-ion batteries, that will help the economy expand for decades to come.

In a way, though, the plant was inadvertently telling a more complicated story, about globalization and the changing nature of commerce. Saft America is a unit of Saft Groupe, a French company with holdings around the world. Sales of lithium-ion batteries have been considerably slower than anticipated, and the factory has yet to turn a profit. The French parent doesn’t expect profitability for another two or three years and has already written down part of its investment on the factory.

Here was a factory built, in part, with U.S. government dollars for the benefit of the local and national economy. Yet the factory, its technology and its patents are all owned by a foreign corporation. Its French chief executive is almost completely detached from the community here in Jacksonville; he did not even attend Obama’s speech. And the factory’s profits, to the extent they ever come, may very well be sent abroad instead of being reinvested here.

The factory visit might also tell a more complicated story about the presidency. It has always been the case that voters credit or, more often, blame the president for the nation’s economic performance. But it is also the case that the president generally has considerably less sway to move the economy than even he might like to acknowledge. And as the economy continues to disperse, that sway may be diminishing further. A president has less power than ever, in either a hard- power (legal/regulatory) or soft-power (cultural) sense, over American chief executives, let alone over the chief executives of multinationals based in France or China or other places where many U.S. employers make their headquarters.

In the assembly room after the speech, Obama acknowledged as much. “When you’re talking about inversions,” Obama said, referring to the practice whereby American companies effectively move overseas, “or you’re talking about C.E.O. perks or the gap between what the assembly-line worker is making compared to what the C.E.O. is making, all those things used to be constrained by the fact that you live in the city, you’re going to church in that city, your kids might be going to the same school as the guy who is working on the assembly line because public schools actually were invested in,” Obama said. “And all those constraining factors have been greatly reduced or, in some cases, eliminated entirely. And that contributes to the trends toward inequality. That contributes to, I think, a divergence between how the people who run these companies and economic elites think about their responsibilities and the policies that they promote with political leaders. And that’s had, I think, a damaging effect on the economy overall.”

Leaning forward in his chair, Obama described the profound structural shifts in the economy over the past two decades that voters often don’t appreciate or acknowledge. “If you are a blue-collar worker, you saw manufacturing head out to China,” he said. “You’re in a town, the plant closes. But — in part because of the housing bubble — a whole bunch of blue-collar manufacturing workers could suddenly shift into construction.”

The underlying economic decay was covered up by cheap credit, as homeowners made up for the shortfall in wage growth with low-interest second mortgages and unprecedented loads of credit-card debt. And that “meant that people felt pretty good in terms of their purchasing power even though their underlying situations hadn’t improved appreciably,” Obama said. Then the bubble bursts, “and suddenly they get washed away.” Those construction jobs have returned slowly, and many of those manufacturing jobs never came back at all.

“They’d be much worse off had we not taken the steps that we took,” Obama said. “But they have a sense that it’s a little more of a struggle for them than it might have been for their parents or for their grandparents.”

Obama considered the problem from a political perspective. “In some ways,” he said, “engaging in those hard changes that we need to make to create a more nimble, dynamic economy doesn’t yield immediate benefits and can seem like a distraction or an effort to undermine a bygone era that doesn’t exist. And that then feeds, both on the left and the right, a temptation to say, ‘If we could just go back to an era in which our borders were closed,’ or ‘If we could just go back to a time when everybody had a defined-benefit plan,’ or ‘We could just go back to a time when there wasn’t any immigrant that was taking my job, things would be O.K.’ ” He didn’t mention Donald Trump or Bernie Sanders by name, but the implications were obvious.

Perhaps the biggest economic shift during Obama’s presidency came from a piece of legislation that wasn’t sold as such. On March 21, 2010, Congress passed the Affordable Care Act, better known as Obamacare.

It was Obama’s boldest piece of legislation and the one that will most likely define him. It has been largely viewed as a social program, a way to provide health insurance to tens of millions of uncovered citizens. But the bill, which affected not just insurance companies but doctors, hospitals and pharmaceutical companies, also had an immediate and growing impact on the economy as a whole. The health care industry accounts for 17.5 percent of the U.S. gross domestic product, and health care spending accounts for 8 percent of the average household budget. Of course, the largest economic challenge most Americans ever confront comes in the form of a sudden health crisis. “In the long term,” Sperling told me, “the Affordable Care Act will actually be seen as one of the great economic accomplishments, not just health care, economic. Because it actually is closing a key part of the insecurity gap.”

In closing that gap, though, Obama has been confronted with a knotty economic and political paradox. The legislation was designed to slow the growth of health care costs, even as it extended coverage. Slowing the growth of an industry that accounts for nearly a fifth of the U.S. economy is inevitably going to mean slowing the growth of the economy as a whole. The legislation was also designed to exert a more subtle economic influence. For most of the postwar era, most Americans received health insurance from their employers, in the form of benefits. If they quit their jobs or were fired, they could lose those benefits, and if they had a pre-existing condition, they could have a hard time getting them back, even if they got a new job with good benefits elsewhere. That meant they would be much less likely to leave a job, and that meant employers could be a little less worried about raising wages, because they had a somewhat captive work force. In the age of the gig economy, more portable insurance could transform the way we work and potentially have a real effect on wages in some sectors.

In 2014, the Congressional Budget Office released a report estimating that the Affordable Care Act would “reduce the total number of hours worked, on net, by about 1.5 percent to 2.0 percent during the period from 2017 to 2024” — a seemingly disastrous outcome for the economy. But, the director of the office, Doug Elmendorf, later wrote, “The reason for the reduction in the supply of labor is that the provisions of the A.C.A. reduce the incentive to work for certain subsets of the population.” In other words, a lot of people worked because they had to, in order to keep their insurance. Now they could quit, even if they were sick; a positive development for them, but with a perverse effect on the economy.

And for all of that, Americans do not yet seem to be feeling the benefits of the new program, in part because the benefits remain uncertain. “If your health care premiums go up by 6 percent, you’re still irritated,” Obama said, “even though the trend lines have been those premiums are going up 15 percent.”

Republicans were unanimously opposed to the bill, and Obama could pass only so much major legislation before the congressional election that many expected to flip House control from the Democrats to the Republicans, as it indeed did. That meant that he had to choose the A.C.A. over any number of other high-priority agenda items, including another stimulus, perhaps in the form of a massive infrastructure bill, which would have given the economy an unambiguous boost. “If you went back a few years, you might say, ‘Well, he should’ve focused even more on pushing through a bigger fiscal stimulus, which he could have if he wasn’t going for the Affordable Care Act,” Rogoff said. “That was a trade-off he made, and it cost him.”

Obama knows it. “The fact of the matter is, is that our failure in 2012, 2013, 2014, to initiate a massive infrastructure project — it was the perfect time to do it; low interest rates, construction industry is still on its heels, massive need — the fact that we failed to do that, for example, cost us time,” Obama said. “It meant that there were folks who we could have helped and put back to work and entire communities that could have prospered that ended up taking a lot longer to recovery.”

After 2010, all that was available to Obama was executive action: The ascendant G.O.P. made anything else nearly impossible. So the president turned more and more to regulatory rule changes and executive orders. He raised the minimum wage for federal contract workers to $10.10; he overhauled immigration policy to protect some illegal immigrants from deportation (the Supreme Court just heard a case to overrule the action); he signed an order calling on government agencies with oversight of industry to find ways to make them more competitive, like pressing cable companies to let customers use cable boxes made by rivals. But without Congress, the big legislative moves, the ones that would really change history, seemed past.

“I can probably tick off three or four common-sense things we could have done where we’d be growing a percentage or two faster each year,” Obama said. “We could have brought down the unemployment rate lower, faster. We could have been lifting wages even faster than we did. And those things keep me up at night sometimes.”

When the president’s motorcade left Saft to head back to Air Force One, I noticed something unusual: The plant’s parking lot was extremely small. It dawned on me that Obama’s tour of the factory, filled with photo ops and handshakes, had included very little interaction with workers. Instead, he was shown machine after machine, mostly operated by computers. At one point, he was introduced to WALL-E, a robot named after the Pixar film that takes battery components from a tray. No employees necessary. This giant mecca of innovation, a physical marvel that if built several decades ago would have easily employed a few thousand people, employs only 300.

It was a scene that underscored a challenge facing the U.S. economy and one that may be the driving factor behind greater inequality: We’re not only losing jobs to overseas competition, we’re losing them to technology. Obama noted the robots, too. “We just saw here those robots were pretty impressive, but also pointed to the direction the economy is going,” he said.

He clearly recognizes the problem — he said he spends a lot of time thinking about it — but he also knows the solutions will come only when he is long out of office. Many citizens, he said, back on Air Force One, “have to worry about retraining at some point in their careers, because they can’t anticipate being in one place for 30 years. The occupational mix in the economy places greater demands on people because it’s changing more rapidly. And all of this makes people feel that they don’t know what’s around the corner.” For whatever sense of “uncertainty” business leaders lament, this may be a much more profound sense of uncertainty.

“It’s one of the reasons that I pursued the Trans-Pacific Partnership,” he said, bringing up the free-trade pact that, uniquely, has divided both parties, “not because I’m not aware of all the failures of some past trade agreements and the disruptions to our economy that occurred as a consequence of globalization, but rather my assessment that most trends are irreversible given the nature of global supply chains, and so we better be out there shaping the rules in ways that allow for higher labor standards overseas, or try to export our environmental standards overseas so that we have more of a level playing field.”

Whether a president can truly improve, or damage, an economy remains an open question. The greatest economic power might in fact remain in the hands of the Federal Reserve. Economists credit the Fed’s policy of keeping interest rates at historic lows with helping to pump up the economy and bring unemployment down. At the same time, the Fed has been blamed for widening inequality, swelling the price of real estate and corporate profits, even as savers and retirees dependent on fixed-income assets have suffered.

That can cut either way in terms of a president’s economic legacy. Critics of Obama, including the new House speaker, Paul Ryan, credit Ben Bernanke, the former Federal Reserve chairman, and Janet Yellen, the current chairwoman, for whatever recovery we’ve had since the crisis, contending it happened in spite of the president. “I think the Federal Reserve has done more,” Ryan said at a January news conference. Frank, for his part, almost jumped through the phone when I mentioned that argument during an interview. “And Bernanke and Yellen were appointed by whom? Neither Bernanke or Yellen would have been able to do what they were doing without his full backing.”