The absence of Social Security from the general-election campaign shows how much the ground has shifted on the issue since 2004, when President George W. Bush put his plan to partially privatize the retirement program at the center of his re-election bid.

Every four years, both parties have at least paid lip service to the idea that Social Security and Medicare, which face looming solvency woes, should be overhauled before they force either unpopular benefit cuts on retirees or a big surge in new federal borrowing.

That hasn’t happened this year due to new forces in both parties.

On the right, GOP nominee Donald Trump has broken with House Speaker Paul Ryan and other party leaders who have long called for overhauling the program now to avoid bigger tax hikes later. Republicans have traditionally been more open to changes in the retirement age and other benefit adjustments. That’s because as the program pays out more in benefits than it collects in revenues, it will be more difficult to preserve benefits without raising taxes or adding to the national debt.

Even after Mr. Bush’s privatization proposals failed to win congressional backing in 2005, Arizona Sen. John McCain embraced a comprehensive effort to address the program’s long-term solvency as the GOP nominee in 2008. Earlier this decade, both parties looked at possible tweaks to Social Security as part of a broader push for a “grand bargain” to cut deficits.

As recently as last year, New Jersey Gov. Chris Christie, positioning himself as a fiscal truth-teller in a crowded GOP field, released an audacious proposal to curb or eliminate Social Security benefits for more affluent retirees.

Mr. Trump, on the other hand, has completely dismissed any talk of changes. “We’re going to save your Social Security without killing it like so many people want to do,” Mr. Trump said at a July rally in Phoenix. Social Security benefits won’t need to be cut “if you can get growth back up,” said Stephen Moore, an economic adviser.

Social Security has been paying out more in benefit dollars than it collects in taxes since 2010. Its annual balances have remained positive due to interest payments it earns on trust-fund assets. By 2020, however, it will pay out more than it collects, even after accounting for interest payments, according to the program’s trustees. After that, it would have to sell government securities to maintain benefit payments, and those trust funds would be depleted by 2034.

Independent analysts say the program’s solvency issues can’t entirely be solved by economic growth because it faces stiff demographic headwinds. There were 2.8 covered workers for each beneficiary last year, down from 3.2 in 2008, and that ratio is set to slide to 2.2 over the next two decades as more in the baby-boom generation retire.

On the left, concerns of income inequality and poor savings for many seniors have prompted many Democrats to call for expanding benefits. Liberals say it’s possible to do this, while shoring up the solvency of the program, by raising the cap on income subject to payroll taxes, which is currently set at $118,500. The cap covers around 82% of wage income, down from 90% when it was created in 1983.

“I do not see how anybody can look at Social Security and say the problem is it’s too generous. If anything, we face a retirement crisis,” said Gene Sperling, an economic adviser to Hillary Clinton.

During the Democratic nomination battle, Vermont Sen. Bernie Sanders pushed Mrs. Clinton to support more generous benefits for retirees and to forswear any cuts. Mrs. Clinton has said she supports enhancing benefits for certain, lower-income retirees.

Over the past week, Mr. Trump has attempted to cast Mrs. Clinton as the candidate who favors cutting Social Security, a charge that isn’t supported by any evidence. Emails released by WikiLeaks show Mrs. Clinton, in paid speeches to private audiences, expressed support for a bipartisan deficit-reduction framework that had been the subject of extensive talks earlier this decade.

Mr. Trump claims the speeches show she favors “knocking the hell out of Social Security,” as he put it last week, but the speech excerpts don’t show she ever spoke directly about the types of entitlement-program changes she would support, making his claim false.