The C-SPAN video from 1995 is grainy, but the audio is clear: Senator Joe Biden is heard bragging about his support for freezing spending on Social Security as part of broader deficit reduction legislation.

“I’m up for re-election this year, and I’m going to remind everybody what I did, at home, which is going to cost me politically. When I argued that we should freeze federal spending, I meant Social Security as well. I meant Medicare and Medicaid. I meant veterans benefits — I meant every single solitary thing in the government,” Mr. Biden says in the video. “And I not only tried it once, I tried it twice, I tried it a third time and I tried it a fourth time.”

The footage is a centerpiece of an attack on Mr. Biden launched last month in the run-up to the Iowa caucuses by his rival for the 2020 Democratic presidential nomination, Senator Bernie Sanders. Mr. Biden has pushed back, and a New York Times review of his record on Social Security over the course of his long Senate career reveals votes in support of protecting benefits as well as cutting them.

The Biden-Sanders dust-up underscores the recent transformation of political debate on Social Security. As recently as 2013, benefit cuts were widely embraced by Mr. Biden and many other centrist Democrats as part of broader bipartisan deals to repair Social Security’s finances or to reduce the federal deficit, which never reached fruition. Progressives fought the benefit-cutting. And that year, they began pushing the idea that benefits should be expanded.