Mr. Lew added, “It left you with the real sense that this could just as easily have failed.”

Twelve years later, the government is again at risk of defaulting on its debt for the first time, and Republicans in the House are again demanding spending cuts in exchange for agreeing to raise the debt limit.. Faced with the highest-stakes economic obstacle of his presidency and left with the searing memory of Obama-era fights, Mr. Biden has held firm that the discussion over raising the $31.4 trillion debt limit must take place separately from spending negotiations, advisers say.

That has not always been the case. Republicans have pointed out in recent weeks that, as a senator, Mr. Biden railed against budget deficits during the Reagan presidency. In 1984, he presented a proposal to freeze federal spending for a year. He said his plan would “shock the living devil out of everyone in the U.S. Senate,” but it went nowhere.

And as vice president, Mr. Biden tied the debt limit and budget issues in 2011, when he was negotiating for the Obama administration. In remarks to reporters on Tuesday, Mr. Biden suggested that he only did that because he had been instructed to get a deal done.

“I got a call that morning at 6 o’clock saying that the Republican leader would only talk to me, and there was no time left,” he said. “And so I sat down, and I got instructions from the White House to settle it. And that was my job. But I had no notice.”

In the spring of 2011, Mr. Biden and a bipartisan group of congressional leaders met frequently to hash out their differences. In early meetings, the group gathered at Blair House, where foreign dignitaries stay when they visit Washington. That summer, Mr. Boehner broke off negotiations, in large part because rank-and-file Republicans would not agree to raise taxes on the wealthy. A complex deal was reached weeks later, leaving Mr. Obama to explain to Democratic voters why he was not able to raise taxes and had agreed to at least $2.4 trillion in spending cuts.