Republicans lobbied their rank and file as well, and the results were far more positive for them than a week ago when they were forced to delay a vote on an earlier measure.
GOP leaders swiftly drew public pledges of support from some first-termers as well as veteran defense hawks — two areas of concern with the agreement.
Rep. C.W. (Bill) Young, chairman of the committee that handles the defense budget, said, "We're confident that we can make this happen without affecting readiness and without affecting any of our soldiers."
There were critics on both sides of the aisle, some of them anguished.
"I did not come to Washington to force more people into poverty," said Rep. Jim McGovern, D-Mass.
"At the end of the day, Washington's spending still has us sprinting toward a fiscal cliff. And this bill barely slows us down," said Rep. Mark Mulvaney, R-S.C.
There is little suspense about the outcome for the debt-limit legislation in the Senate on Tuesday.
A member of the Republican leadership in the Senate predicted strong GOP support. "Maybe 35 (of 47) will support it in the end. There will be some who will pull back," said Sen. Mike Crapo of Idaho.
Already, the legislation was emerging as an issue in the 2012 presidential campaign.
Rep. Michele Bachmann of Minnesota and former Massachusetts Gov. Mitt Romney announced their opposition, while Newt Gingrich issued a statement without saying how he would vote.
The final legislation reflected the priorities of the two political parties.
It would immediately increase the debt limit by $400 billion, with another $500 billion envisioned unless Congress blocks it. At the same time, it would cut more than $900 billion over 10 years from the day-to-day operating budgets of Cabinet agencies. For the budget year that begins Oct. 1, spending would be held $7 billion below current levels.
The measure also establishes a 12-member House-Senate committee that will be charged with producing up to $1.5 trillion in additional deficit cuts over a decade. If the panel succeeds, Congress will be required to vote on the recommendations without possibility of changes.
If the panel deadlocks or fails to produce at least $1.2 trillion in deficit savings, then spending cuts are to take effect across much of the federal budget. The Pentagon, domestic agencies and farm subsidies would be affected, as would payments to doctors and other Medicare providers. But individual benefits under Social Security, Medicaid, Medicare and programs for veterans and federal retirees would be exempt.
At the same time, the debt limit would rise by at least another $1.2 trillion, and perhaps — depending on the results of the committee's work — as much as $1.5 trillion.
Additionally, the legislation requires both the House and Senate to vote on a balanced-budget amendment to the Constitution.
The measure also increases funding for Pell Grants for low-income college students by $17 billion over the next two years, financed by curbs on federal student loan subsidies.
The result of weeks of negotiations and harsh arguing, the final result represented a product of divided government that gave neither side everything it wanted. Leaders in both parties were emphatic on that point.
"As with any compromise, the outcome is far from satisfying," conceded Obama in a video his re-election campaign sent to millions of Democrats. In a tweet, the president was more positive: "The debt agreement makes a significant down payment to reduce the deficit — finding savings in both defense and domestic spending."
Associated Press writers Jim Abrams, Stephen Ohlemacher, Alan Fram, Julie Pace, Donna Cassata, Andrew Taylor and Larry Margasak contributed to this report.
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