Ariens Co., a maker of lawnmowers and snowblowers, faces a bottleneck in its plans to raise production 40%. It can’t find enough workers.

The Brillion, Wis., company bused some Somali refugees from nearby Green Bay to help, but they weren’t enough, and it is spending up to $15,000 a month on recruiting.

“We see the demand right in front us,” said Chief Executive Dan Ariens. “It’s very frustrating.”

His lament points to an issue at the heart of President Donald Trump’s economic agenda. The president has laid out a goal of getting the U.S. economy, which has expanded at less than a 2% average rate for the past decade, to grow at above a 3% rate over the long term.

Two stubborn obstacles stand in his way. The work force isn’t producing enough new workers, and the productivity of those working isn’t growing fast enough.

In the long term, an economy can’t expand faster than the combined growth rates of its working population and their output per hour. That combined number, in many economists’ projections for the next decade, is about 1.8%. This is also the long-run growth rate projected for the economy by Federal Reserve officials.

Mr. Trump’s advisers say their policies can deliver 3% to 4% growth year after year, the kind of prosperity the U.S. saw during the 1980s and 1990s—in effect expanding what is considered the economy’s long-term potential.

A note on a framed newspaper article in Treasury Secretary Steven Mnuchin’s office is even more ambitious. The article announced his Cabinet selection, and Mr. Trump signed it in felt-tip pen with the added note “5% GDP.”

Faster growth could push up household incomes, which are stuck below their 1999 peak when adjusted for inflation. Such growth would also make it easier for the administration to secure large cuts in corporate and individual tax rates, boost military spending, and maintain Social Security and Medicare without running larger deficits. Asked in April about potentially higher deficits from rate cuts in the tax plan, Mr. Mnuchin said, “The plan will pay for itself with growth.”

If the economy expands at around a 3% rate over the next decade—a projection Mr. Mnuchin says the administration will make in its budget proposal later this month—government revenue over that time should be $3.7 trillion more than currently forecast, according to estimates by economists at Goldman Sachs Group Inc. The projection assumes no change in tax rates.

That would be enough money to build 292 aircraft carriers. It would fund 28 million additional months of Social Security payments for the average beneficiary.

Mr. Trump wants to spur the economy partly by improving the nation’s trade position. Less red tape could help business operate more efficiently. A tax overhaul could give companies more incentive to invest and give individuals more desire to work, not to mention more disposable income to shop with.

Trump advisers also are hopeful that improved confidence and short-term economic news would spur capital spending that makes business more productive.

Finding the labor for this higher-functioning economy could be a challenge. Over the past decade, the population aged 25 to 54, known as the prime age, has been growing at just 0.1% annually. When the U.S. had consistent 3% economic growth in the 1980s, the prime-age population was expanding at a brisk 2.2% rate, thanks to the post-World War II baby boom.

Work-force participation rates, meanwhile, have flattened out lately for women and declined for decades among men.

At Macy’s Inc., Chief Executive and President Jeff Gennette hit on a plan for growth with a 2015 agreement with Luxottica Group SpA to open LensCrafters shops in department stores. The plan is hobbled by a shortage of optometrists. “We are taking all of the graduating classes right now, and it is going to take us a full year to…satisfy the expansion that we have,” Mr. Gennette said at a retail conference.

Without faster growth in workers, the labor force would need to churn out goods and services much more productively to give the economy room to grow at a 3%-a-year rate over an extended period. The trend is the opposite. Workers’ output per hour in the nonfarm business sector has been increasing only by 0.7% a year since 2010.

Many economists see that picking up in coming months, perhaps doubling. Meeting Mr. Trump’s objective, though, would need “the type of growth we often refer to as productivity miracles,” said Michael Feroli, chief U.S. economist at J.P. Morgan Chase & Co.

The contours of growth and the labor market are likely to influence the pace by which the Fed drains its easy money from the financial system. If growth advances and productivity does too, policy makers may be able to keep interest rates lower for longer because productivity growth holds down inflation. Companies can boost profit margins and hold down costs, and thus inflation, when they can produce more goods and services with fewer workers.

If, on the other hand, the administration’s policies boost demand without drawing in new workers or raising their productivity, the growth that results could be harder to sustain because it would produce inflation. The Fed would feel additional pressure to raise interest rates to prevent the economy from overheating.

With the unemployment rate now at 4.4% and operating at a level economists consider to be “full employment,” meaning the economy produces as many jobs as it can without spurring inflation, the labor market provides little room for the kind of economic surge that marked the 1980s.

“Strong growth during the Reagan years was driving unemployment from 10% to full employment. We can’t do that trick again,” said Joel Prakken, senior managing director of Macroeconomic Advisers, a forecasting firm.

The Trump administration has faced internal tensions over its growth forecast. Officials ultimately settled on economic growth forecasts in its upcoming budget proposal to Congress that will show the economy reaching 3% growth after two years, according to Mr. Mnuchin.

The president is pushing some policies that work against economic growth. Relatively low birthrates and an aging population mean immigration is the source of nearly all of the work force’s net increase, so its growth rate would be even lower if legal immigration were curbed. That makes boosting productivity all the more important if the economy is to get onto a faster growth plane.

Home builders are wrestling with both issues. The real-estate crisis a decade ago washed many skilled workers out the construction labor force. At Camden Property Trust , this dearth has extended the time it takes to build a low-rise apartment complex to 24 months from 18.

“I’m often paying unskilled workers more money, and I have to pay someone else to come in and fix crooked walls and moldings and cabinets that don’t connect,” said CEO Ric Campo of Camden, which operates in 16 markets and is based in Houston.

Camden uses efficiencies such as prefabricated concrete building panels and roof trusses, “but there hasn’t been a huge breakthrough yet where we can lower costs dramatically,” said Mr. Campo. “You have a nail gun instead of a hammer, OK? But you still have to line it up and pull the trigger.”

Productivity in construction has contracted at a 1% annual rate since 1995, according to a study by McKinsey Global Institute, the research arm of McKinsey & Co., due in part to reliance on unskilled workers and in part to government red tape.

Joel Shine, chief executive of builder Woodside Homes Inc., visited Kyoto, Japan, to see how firms there use automation in home construction. He thinks it would take at least a decade for the innovations to become mainstream in the U.S., in part because they would require building-code changes.

State and local rules often play as big a role for his business as the federal government. Higher permitting fees, for instance, have raised construction costs in California towns. “There are a lot of places if you gave me a raw lot for free—for free!—I could not even come close to building an entry-level house,” Mr. Shine said.

Immigration restrictions would make growth harder, he added. “We’re somewhat uniquely capable of helping the administration get to where they want to go, but they can’t ask us to do that and then make immigration impossible,” Mr. Shine said.

White House Budget Director Mick Mulvaney, who once ran his family’s real-estate business, disputed that premise and pointed to millions of prime-age workers who aren’t in the labor force. “If you created economic opportunity and jobs that they want, they would come back,” Mr. Mulvaney said. “So I’m not worried about the tightness of the labor supply.”

If that proves insufficient, the onus will be on productivity. It isn’t easy either to measure or to predict. The U.S. economy enjoyed a boom in productivity from around 1995 through 2004, a spurt few economists foresaw. By 2003, the conventional wisdom had reversed and economists polled by The Wall Street Journal were expecting productivity growth to continue unimpeded. Instead, it slumped.

The weakness reflects a sustained deceleration in the pace of innovation and investment. Capital investment growth slowed sharply during and after the 2007-09 recession.

Goldman economists see evidence that the slowdown has been cyclical, driven by the financial crisis, and now could be changing. Mr. Ariens, the snowblower executive, offers one bit of evidence. He plans to spend $9 million this year on factory upgrades, including advanced metal-stamping machines that could do the work of a dozen workers.

Some productivity optimists say gains from new technology will build in the years ahead. They see businesses incorporating a backlog of innovations in artificial intelligence, from self-driving vehicles to the processing of routine clerical work.

A paper from four growth specialists published by the Brookings Institution in March takes a dimmer view. It maintains that almost the entire shortfall in output during the recent expansion reflects long-term forces unrelated to the financial crisis and recession, including a drop in a measure of economic dynamism called “total factor productivity.” That measure reflects how efficiently labor and capital are used.

Many economists say well-designed cuts in taxes and regulations could deliver a lift to the U.S. economy that would nudge growth to 3% for a year or two. They are less confident it could be sustained. Dale Jorgenson, a Harvard University economist who specializes in growth accounting, thinks that the economy should expand 1.8% annually over the next decade, but that a well-designed tax-code overhaul might boost the long-term growth rate to 2.4%.

“In some respects,” said James Stock, a Harvard colleague and veteran of the Obama administration, “2.5% growth could be the new 4%, in that it would still be a significant accomplishment.”