The last time President Obama signed on to a plan to save Social Security, nearly five years ago, he agreed to a proposal that would have reduced the growth of benefits.

But now, with Sen. Bernard Sanders of Vermont leading a populist charge in the Democratic presidential primary for expanding retirement benefits, the president has changed his tune and climbed aboard the socialist’s bandwagon.

“It’s time we finally made Social Security more generous,” Mr. Obama said last week in Elkhart, Indiana. “We could start paying for it by asking the wealthiest Americans to contribute a little bit more. They can afford it. I can afford it. We can’t afford to weaken Social Security.”

Mr. Obama is not only calling for higher taxes to boost Social Security payments, but he also is trying to rewrite history by repudiating a proposal to reduce beneficiaries’ cost-of-living increases, which he agreed to in 2011.

“That is something that Republicans wanted,” said White House press secretary Josh Earnest. “That is not something that the president ever supported; it’s something that the president acknowledged that could be part of a grander bargain that would do a bunch of things, including strengthening Social Security and reducing the deficit. Unfortunately, Republicans were never willing to actually do that.”

Critics say Mr. Obama, with seven months remaining in office, is more interested in crafting his legacy than in actually shoring up the retirement fund.

“It’s clear the president is worried about his legacy, and his response is to mimic the socialist senator from Vermont,” said Doug Andres, a spokesman for House Speaker Paul D. Ryan, Wisconsin Republican.

When reporters noted that Mr. Obama had included in past budgets the proposal to reduce Social Security cost-of-living increases, known as “chained CPI,” Mr. Earnest made it clear how the White House wants to be remembered in history.

“It’s very important for people to understand, the president does not support, has never supported this so-called chain CPI proposal,” he said. “The reason the so-called chained CPI was included in our budget was not an indication that we supported that policy proposal. That has never been the position of the administration, and it’s certainly never been the position of the president.”

A former aide to John A. Boehner, the House speaker with whom the president reached the agreement in 2011, called the White House’s revisionism absurd.

“Both the president and the speaker agreed to support the CPI fix early in the discussions,” said the aide, who requested anonymity. “In fact, they agreed to claim it as a joint proposal to help sell their respective members and gain support for this essential, albeit not necessarily popular, fix.”

Robert Bixby, executive director of the Concord Coalition, a nonpartisan group that advocates for responsible fiscal policy, said the White House is playing word games retrospectively about lowering Social Security benefits.

“It was something that the president was at least willing to accept; it was in his budget as a proposal,” Mr. Bixby said in an interview. “There are probably a lot of Republicans who are now regretting that they didn’t take the White House up on that offer when it was on the table, because it’s clearly off the table now.”

He said Mr. Obama’s late-term conversion in favor of expanding benefits is meaningless from a policy perspective.

“It would be more helpful from a fiscal point of view in calling attention to the fact that the system has an enormous shortfall,” Mr. Bixby said. “This is more of an election-year type of thing that plays to the base. Raising benefits would throw the system even further out of whack. Raising taxes to pay for it wouldn’t help the problem that we’ve already got.”

Hillary Clinton, who came over in February to Mr. Sanders‘ proposal not to cut benefits for anyone, tweeted her approval of Mr. Obama’s move. “We can never let Republicans cut or privatize Social Security. We should protect and expand it,” she said Friday.

The proposals on the left to raise retirement benefits without explaining how to pay for them is exasperating fiscal analysts, who say the government can’t keep postponing Social Security’s day of reckoning.

The Committee for a Responsible Federal Budget said that although Mr. Obama didn’t outline the size of tax hikes or benefit increases, “broad-based benefit increases would not be the best use of resources and would put the cart before the horse in terms of ensuring solvency.”

“In addition, increasing taxes on the rich would help Social Security’s finances but would not fully ensure 75-year solvency and would become a more inadequate solution over time, especially if it is enacted along with benefit increases,” the group said.

The committee, consisting of former top government officials such as Mitch Daniels, Leon E. Panetta and Maya MacGuineas, said Mr. Sanders‘ proposal to expand benefits would cost 1.3 percent to 1.4 percent of payroll when fully phased in, the equivalent of at least $1.2 trillion over 10 years.

“For that cost, it would be possible to fully repeal the non-defense sequester, make college debt-free, double National Institutes of Health research funding, make community college free, establish universal pre-K, and fully fund the Highway Trust Fund,” the group said.

About 8 percent of Social Security beneficiaries 62 and older live in poverty, the committee said, and 13 percent of beneficiaries have incomes less than 125 percent of the poverty line.

“Certainly more could be done to enhance benefits for these and other vulnerable populations; for example, by creating a new minimum benefit, making the benefit formula more progressive, and/or expanding benefits for widow(er)s,” the group said. “But the case for broad-based benefit expansions — including for very wealthy beneficiaries — seems weak.”