At the same time, Representative Nancy Pelosi of California, the former speaker and current Democratic leader, was noncommittal about the plan, suggesting that Democrats might not rally behind it. “I look forward to reviewing the legislation with my caucus to see what level of support we can provide,” she said in a written statement.

Senior White House officials said they were hopeful that Congressional leaders from both sides would manage to sell the deal to their parties. While “there are some Democrats who simply don’t believe in the necessity of deficit reduction,” one administration official said, “most do. I think it’s important as a party to show Americans that we’re serious about deficit reduction.”

The Senate seemed an easier sell. Senator Mike Johanns, Republican of Nebraska, said that from the terms of the deal described to him, “I think I will be satisfied and supportive.” After years of work, he noted, Congress has become “serious about cuts in spending.”

As conversations flowed between the White House and Capitol Hill early Sunday, Mr. Reid publicly embraced the compromise that would tie deep spending cuts to a debt ceiling increase even though some Democrats believed the White House has given too much ground to Mr. McConnell and Mr. Boehner.

While lawmakers awaited word of an agreement, talks dragged on. Congressional and administration officials attributed the delay to efforts by Mr. Boehner, Republican of Ohio, to limit immediate reductions in the Pentagon budget and better protect it from future cuts in order to cement votes from defense hawks. He needs those votes to win approval of the plan in the House.

Officials said that Mr. Boehner ultimately did not gain much and that the dispute was settled through an agreement to expand the definition of “security-related” spending to include departments beyond the Pentagon, spreading out potential cuts to the Department of Homeland Security and other agencies.

The tense, last-minute negotiations were taking place against a backdrop of uncertainty, with a looming threat of a costly downgrade of the nation’s credit rating and with investors worried about the global economic impact of a possible default. The political stakes were unusually high as well, with leaders in both parties staking out positions that may well be central to their re-election chances in 2012. Vice President Joseph R. Biden Jr. was on the phone all weekend with Republican leaders of the House and Senate.