After the 2004 elections, a Republican president, newly returned to office, decided the political moment was right to overhaul Social Security, making it more like private retirement plans in a bid to prevent it from going bankrupt in the future. Two years and a bruising political fight later, Democrats took back the House and Senate from Republicans.

Democrats now believe history may be about to repeat itself.

Elon Musk, the multibillionaire overseeing the Trump administration effort to drastically shrink government, has derided the nation’s most popular federal program as a sketchy pyramid scheme while pushing to close offices and eliminate thousands of jobs of those who administer the program. In doing so, he has touched a topic that has traditionally been known as the third rail of American politics. And Democrats, who increasingly regard Mr. Musk as a more opportune political target than even President Trump himself, have rushed to highlight what they consider to be a major political blunder.

“They don’t learn,” Senator Chuck Schumer of New York, the Democratic leader, said of Republicans as his party pounced on the issue. “Their biggest mistake was going after Social Security when George Bush was president. And now they are doing it again.”

Illustrating the emphasis Democrats intend to put on the subject, Senator Elissa Slotkin, the Michigan Democrat who delivered her party’s rebuttal to Mr. Trump’s congressional address on Tuesday night, hit on Social Security as well, using it to cast doubt on the president’s vows not to touch the federal retirement program.

“The president claims he won’t, but Elon Musk just called Social Security the biggest Ponzi scheme of all time,” she said in her remarks, quoting a social media post by Mr. Musk.

Democrats were already pressing Republicans on potential cuts to Medicaid, the government health coverage program for lower-income Americans, but they view threats to Social Security as having broader resonance.

Congressional Republicans respond that Democrats are distorting the Trump administration’s — and their — position on Social Security and that they are simply trying to bolster the finances of the program to guarantee that it won’t run out of money, allowing future generations, like past ones, to get the money they paid in.

“We need to make sure that Social Security is strengthened and saved for the future so that everyone who’s paid in can get it,” said Senator John Barrasso of Wyoming, the No. 2 Senate Republican.

Social Security has long been the political backbone of the Democratic Party. For years, Democrats have capitalized on the slightest hint of any attempt to dismantle or privatize it, as they did when President George W. Bush pushed the idea in 2005, much to the detriment of his party’s midterm election fortunes.

The issue is so volatile that when Senator Rick Scott, Republican of Florida, put forward a policy agenda during the 2022 midterm elections that would have theoretically required the program to expire and be re-evaluated, he was immediately repudiated by Republican leaders and eventually had to disavow his own plan.

Mr. Trump has repeatedly emphasized that he has no plans to tinker with Social Security or Medicare. But Democrats see something afoot with Mr. Musk’s derogatory comments and Mr. Trump’s claims that the program is riddled with fraud.

Despite multiple reviews that have found Social Security to be one of the better-run federal programs with a record of never missing payments, Mr. Musk has characterized the program as riddled with fraud and waste.

Mr. Trump emphasized that theme in Tuesday night’s address, saying that millions of obviously long-dead beneficiaries remain on the Social Security rolls. But the claim he and Mr. Musk make that benefits still flow to those people has been widely debunked. The agency says that it is a data recording problem, and has reported that just under 90,000 people 99 years or older received Social Security benefits in December — slightly more than the 85,000 Americans over the age of 100 recorded by the Census Bureau.

Still, Democrats see the focus by Mr. Musk and Mr. Trump on erroneous claims of fraud as laying the groundwork for a benefit review that could affect those lawfully receiving monthly benefits as Republicans search for ways to offset the cost of hugely expensive tax cuts.

Democrats say an equal threat to the program are plans to reduce the work force that had already shrunk, including an effort to pare down as many as 7,000 employees while consolidating regional offices and ending the leases on dozens of field offices around the country. They say the loss of personnel and the shuttering of offices would be tantamount to denying benefits to applicants who would face long waits to talk to advisers or to receive their assistance.

Senator Patty Murray, Democrat of Washington, said such delays would break the inherent promise of Social Security that Americans can collect what they contributed.

“Part of that promise means being able to get on the phone with an actual human being without having to wait on hold for an hour or more, visit an in-office person to help you get your benefits without having to jump through hoops or drive hundreds of miles,” Ms. Murray said. “But Trump and Elon are decimating the Social Security Administration and without adequate staff at the agency, there will be people who cannot get their benefits period.”

Some Republicans also expressed concern about how cuts could affect the level of service their constituents receive.

“I do know that it is a whole lot easier to work your way through Social Security benefits if you’re doing it in person with somebody who is well trained in how the system works,” said Senator Mike Rounds, Republican of South Dakota. “Trying to do any of that stuff online is much more difficult.”

But Mr. Rounds also credited Mr. Musk with bringing attention to the fiscal condition of Social Security, which is in such dire financial trouble that benefit cuts could come within a decade if nothing changes.

“He’s at least ringing the alarm that the rest of us have tried to do,” said Mr. Rounds, who added that obvious fixes were available.

Multiple ideas are circulating to stabilize the program, such as lifting the current $176,100 cap on the amount of pay that is taxed for Social Security.

“If Congress eliminated the payroll tax cap for individuals with annual income in the millions of dollars — an amount Elon Musk makes every two hours — and collected the money they are illegally evading in taxes, Social Security would be fully funded for decades,” said Senator Ron Wyden of Oregon, the senior Democrat on the Finance Committee.

But no one on Capitol Hill is talking seriously about raising that cap any time soon. For now, the push by Mr. Musk to shrink the agency and the beneficiary rolls will guarantee that Social Security remains at the center of the clash over federal spending in the coming months and next year’s elections.