President Obama and Congressional leaders of both parties said late Sunday that they had agreed to a framework for a budget deal that would cut trillions of dollars in federal spending over the next decade and clear the way for an increase in the government's borrowing limit.

With the health of the fragile economy hanging in the balance and financial markets watching closely, the leaders said they would present the compromise to their caucuses on Monday morning in hopes of enacting it before a Tuesday deadline to avert default.

Even as the president was speaking from the White House on Sunday night, Speaker John A. Boehner was on a conference call with House Republicans, trying to sell them on the proposal he had signed off on only minutes before.

Since he is likely to lose the most conservative elements of the caucus, Mr. Boehner faces the task of framing the pact as friendly enough to Republican principles to win over a significant group of his rank-and-file without alienating Democrats he will need to push it over the top.

President Obama, in a hastily called appearance with reporters that ended a day of uncertainty, said that the compromise would "allow us to avoid default and end the crisis that Washington imposed on the rest of America."

"It ensures also that we will not face this same kind of crisis again in six months, or eight months, or 12 months," he said. "And it will begin to lift the cloud of debt and the cloud of uncertainty that hangs over our economy."

Just before Mr. Obama spoke on television, the two Senate leaders, Harry Reid and Mitch McConnell, took the floor to endorse the pact as well.

"I am relieved to say that leaders from both parties have come together for the sake of our economy to reach a historic, bipartisan compromise that ends this dangerous standoff," said Mr. Reid, the majority leader.

The tentative agreement calls for at least $2.5 trillion in spending cuts over 10 years, a new Congressional committee to recommend a deficit-reduction proposal by Thanksgiving, and a two-step increase in the debt ceiling.

The announcement concluded a tumultuous 24 hours that saw hopes rise Saturday night over the prospects of a deal that might have concluded the budget stalemate. By Sunday, worry set in again as lawmakers and White House officials struggled to hammer out the fine points of an agreement that must clear a Senate controlled by Democrats as well as by the Republican House.

If the deal clears Congress, with its new special joint committee to explore deficit reduction, it will ensure that the size and scope of the federal government and the tension between spending and taxes will remain front and center in the Washington debate headed into the 2012 election.

Markets reacted favorably to the announcement. Asian markets jumped on news of the deal. The Nikkei was up 1.7 percent in early trading; the dollar rose about 1.4 percent against the Japanese yen.

The agreement came after a day of wrangling over Pentagon cuts, and it still must win majority support in the Senate and the House, with the House providing a particular challenge.

On the conference call, Mr. Boehner sought to portray the new agreement as one heavily tilted toward the Republican call for no new revenue, and he said it met the goal of instituting cuts greater than the amount of the debt limit increase. In a presentation, he said the pact would prevent a "job-killing default" - a warning to lawmakers that failure to raise the limit could add to the bleak employment picture.

"Our framework is now on the table that will end this crisis in a manner that meets our principles of smaller government," said Mr. Boehner, who said he hoped to get the legislation onto the House floor as quickly as possible.

As conversations flowed between the White House and Capitol Hill, Mr. Reid earlier Sunday publicly embraced the compromise that would tie deep spending cuts to a debt ceiling increase, though his plan to bring it to a vote as early as Sunday was put off, as was a tentative meeting of Senate Democrats to review it.

According to Congressional and administration officials, the delay was attributable 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.

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.

If the compromise were to be nailed down, attention would immediately turn to selling it to the rank-and-file. The leadership was anticipating objections from Republicans that the plan did not go far enough while Democrats were wary that Medicare spending would take a hit.

Despite the remaining political and procedural hurdles, the predominant mood on Capitol Hill was one of cautious relief that the gears were turning to produce legislation that would eliminate the threat of a potential government default after Tuesday.

Referring to the tortuous negotiations, Senator Dianne Feinstein, Democrat of California, said: "Sausage making is not pretty. But the sausage we have, I think, is a very different sausage from when we started."

She noted that the proposed caps on federal spending, combined with creation of a new evenly divided panel to cut the deficit further, could fundamentally change federal finances.

But not everyone was pleased. "It may be the best we can do," said Senator Jeff Sessions of Alabama, the senior Republican on the Budget Committee. "But I do not think it's enough."

With the talks appearing to make progress, the Senate blocked a Democratic proposal for a debt limit increase on a vote 50-49, falling 10 votes short of the 60 required to limit debate. But all attention was on the negotiations.

White House aides were in a flurry of meetings as they prepared for the prospect of announcing a deal. After weeks of political theatrics and Congressional votes that appeared to go nowhere, the mood at the White House on Sunday afternoon was one of cautious optimism.

But Obama administration officials are also aware of the precarious risk the president was running if he strikes a deal that Congressional Democrats find hard to swallow. Mr. Obama's top political aides, including Vice President Joseph R. Biden Jr. and the senior White House adviser David Plouffe, were on the phone Sunday afternoon with Democratic leaders, who gathered in the Capitol Sunday afternoon to explore the outlook for the measure.

In an e-mail to Republican House members, Mr. Boehner noted that "discussions are under way on legislation that will cut government spending more than it increases the debt limit, and advance the cause of the balanced budget amendment, without job-killing tax hikes."

"Those talks are moving in the right direction, but serious issues remain," the speaker wrote.

Under the plan as described by officials briefed on its outline, the debt limit would be increased by $900 billion in the first installment, subject to a Congressional vote of disapproval that Mr. Obama would be able to veto. To prevent a default, $400 billion would be added immediately.

A second increase of $1.2 trillion to $1.5 trillion would be available subject to a second vote of disapproval by Congress. At the same time, a new joint Congressional committee would be created to find a like amount of cuts.

If the evenly divided committee failed to agree on a plan, Congress would either have to approve a balanced budget agreement or accept an across-the-board cut in spending in line with the committee's goal, with 50 percent of the savings coming from the Pentagon beginning in 2013. Medicare would also sustain cuts, though the reductions would be capped.

The rationale for picking such favored programs as the Pentagon for Republicans and Medicare for Democrats was to provide a strong incentive for the new committee to avoid a deadlock and deliver a deficit reduction plan that could clear Congress.

According to Democratic officials close to the talks, among the final sticking points that were worked out were efforts to exempt the Medicaid program from reductions under the automatic spending reductions and make certain that the Medicare cuts hit health care providers, not beneficiaries.

Negotiators did agree that any deal would not include language that could lead to a new formula for the annual cost-of-living adjustments for Social Security beneficiaries that could save more than $100 billion in the first 10 years. While many economists have long said the existing formula overstates inflation, many Democrats oppose any change that would reduce benefits from current law.

Dropping the proposal from the White House-Congressional talks reflected in part the influence of Representative Nancy Pelosi, the Democratic minority leader, whose negotiating hand has been strengthened since she will have to deliver a significant number of Democratic votes for House passage of any solution given the likelihood that Mr. Boehner will face significant loss of Republican votes.

Senators said they expected that the plan as it was being portrayed would attract a bipartisan vote even though both Democrats and Republicans would have reservations.

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."