Despite the tension and uncertainty that has surrounded efforts to raise the debt ceiling, the vote of 269 to 161 was relatively strong in support of the plan, which would cut more than $2.1 trillion in government spending over 10 years while extending the borrowing authority of the Treasury Department. It would also create a powerful new joint Congressional committee to recommend broad changes in spending — and possibly in tax policy — to reduce the deficit.

Scores of Democrats initially held back from voting, to force Republicans to register their positions first. Then, as the time for voting wound down, Representative Gabrielle Giffords, Democrat of Arizona, returned to the floor for the first time since being shot in January and voted for the bill to jubilant applause and embraces from her colleagues. It provided an unexpected, unifying ending to a fierce standoff in the House.

The Senate, where approval is considered likely, is scheduled to vote at noon on Tuesday and then send the measure to Mr. Obama less than 12 hours before the time when the Treasury Department has said it could become unable to meet all of its financial obligations.

The deal sets in motion a substantial shift in fiscal policy at a moment when the economic recovery appears especially fragile. Although the actual spending cuts in the next year or two would be relatively modest in the context of a $3.7 trillion federal budget, they would represent the beginning of a new era of restraint at a time when unemployment remains above 9 percent, growth is slowing and there are few good policy options for giving the economy a stimulative kick.

The precise impact on the economy is a matter of debate. Proponents of spending restraint say that the economy will benefit in the long run from getting the deficit and the accumulated national debt under control, and that failure to act now would risk long-term decline in the nation’s economic might. Others say that by foreclosing the option of using government spending to counteract economic weakness, the country is increasing the risk of persistently high unemployment and even another recession.

The negotiations exposed deep fissures within both parties. In the end, 174 Republicans and 95 Democrats backed the deal, and 66 Republicans and 95 Democrats voted against it. But Republicans and Democrats alike made clear they were not happy swallowing the agreement, which was struck late Sunday between the bipartisan leadership of Congress and President Obama.

Top lawmakers characterized the bill as a must-pass measure needed to prevent a potentially crippling blow to the struggling economy.

“The default of the United States is not an option,” said Representative Steny H. Hoyer of Maryland, the No. 2 Democrat.

Mr. Hoyer urged lawmakers to vote not as members of either party, but as “Americans concerned about the fiscal posture of their country, about the confidence that people around the world have in the American dollar.”

Republicans, while expressing dissatisfaction that the measure did not provide more savings, said it was a modest but useful first step in reversing the government’s spending course and claimed they had prevailed by keeping the agreement free of new revenue and offsetting the increase in the debt limit with spending cuts.

“I would like to say this bill solves our problems,” said Representative Jeb Hensarling of Texas, a prominent fiscal hawk in the Republican leadership. “It doesn’t. It is a solid  first step.”

Worried about defections by conservatives and liberals alike, leaders of both parties gathered their members for briefings to explain the proposal. Speaker John A. Boehner met specially with Republicans on the House Armed Services Committee, an important voting bloc whose members were raising alarms about potential spending cuts for the Pentagon.

Democrats, many disgruntled over what they saw as a White House-negotiated giveaway to Republicans, heard from Vice President Joseph R. Biden Jr., who told House and Senate members in separate meetings that the administration had to cut the deal with uncompromising Republicans to avoid a default.

Mr. Biden spent hours behind closed doors in the Capitol. According to participants in the meetings, he mixed listening and gentle persuasion, urging Democrats to back the plan.

Administration officials fanned out to make a case that the deal’s structure — with a trigger that could force deep cuts in military spending as well as in domestic programs if the two parties cannot agree on how to reduce the deficit further — provided Democrats with more leverage to push for higher tax revenue as part of the solution rather than relying totally on spending cuts.

But many Democrats said they saw it as a deal negotiated on the backs of poor and working-class Americans, with no sacrifice by the rich in the form of tax increases.

“I wouldn’t call it anger, but we are perplexed that it has turned out like it has,” said Representative G. K. Butterfield, Democrat of North Carolina, grimacing as he left the Biden meeting. “But we’ve run out of options and we know the consequences. I’ve heard horror stories from the Great Depression. I don’t want my fingerprints on that.”

Jeff Zeleny and Jennifer Steinhauer contributed reporting.

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