Representative Hakeem Jeffries of New York, the Democratic leader, gathered his lawmakers in the Capitol on Wednesday morning, along with top White House officials who had helped broker the deal. He urged them to back the compromise, arguing that Mr. Biden had successfully fended off the worst of Republicans’ demands.

“I made clear that I’m going to support legislation that is on the floor today,” Mr. Jeffries told reporters at a news conference after the meeting. “And I support it without hesitation or reservation or trepidation.”

Still, progressive Democratics were openly agonizing about supporting the bill.

“This has been a hostage situation,” Representative Greg Casar of Texas said. “We’re going to get out of the hostage situation. I appreciate the president negotiating down the ransom payment for the hostage. But I think it’s appropriate for progressives to say we never want to be in this situation again.”

Mr. McCarthy and his negotiators also sought to sell their conference on the compromise on Tuesday night, saying that Democrats had not scored any victories in the bipartisan talks and that his team had fought strenuously against the White House to prevent tax increases and secure new work requirements for social safety net programs, according to lawmakers who attended.

“In a progressive-left administration and Democratic Senate, we will now have new work requirements,” Representative Patrick T. McHenry of North Carolina, one of the Republican negotiators, said at a news conference following the meeting. “We have conservative reforms that are included in this debt ceiling, and these things should help Republicans rally to the cause.”