Obama said there are "still some very important votes to be taken" but "I am here to announce the leaders of both parties in both chambers have reached an agreement to reduce the deficit and avoid default."
Obama said the deal includes an initial $1 trillion in cuts over 10 years and also will establish a bipartisan committee of Congress that will report by November on further deficit-cutting measures for an "up-and-down vote."
"In this stage, everything will be on the table," Obama said.
He acknowledged neither party will be happy with all of the agreement, but it "ensures we also will not face this kind of crisis again in six months or in eight months or in 12 months."
"We're not done yet," he said, urging members of both parties to "do the right thing" and support it.
"It will allow us to avoid default. It will allow us to pay our bills. It will allow us to start reducing our deficit in a responsible way ... ."
The president's announcement came shortly before concerned world markets opened for business Monday.
Senate Majority Leader Harry Reid said just minutes earlier the framework of a compromise had been reached and leaders of both parties would present the deal to their caucuses Monday.
"My message to the whole world tonight, is that this nation and this Congress are moving forward and we're moving forward together," the Nevada Democrat said.
Senate Minority Leader Mitch McConnell, R-Ky., said his GOP colleagues would be presented the details and "to give everyone a chance to weigh in." He said he had "a high degree of confidence" the deal can pass.
Speaker John Boehner, R-Ohio, had told his members earlier the debate was "moving in the right direction but serious issues remain," Politico reported.
Before the announced compromise, Reid's proposal, which would cut trillions from the federal budget without tax increases, had been favored by a 50-49 Senate vote, far short of the 60 needed to end debate and move the measure.
All Republicans voted no except Scott Brown of Massachusetts. All Democrats voted yes except the two most conservative, Joe Manchin of West Virginia and Ben Nelson of Nebraska, the report said.
But independent Bernard Sanders of Vermont, reflecting growing anger on the left with Obama administration compromises, also voted no.
Earlier Sunday, McConnell, said on CNN's "State of the Union" he was "very, very close to being able ... to recommend to my members that this is something that they ought to support."
McConnell said the deal might not include any tax increases, something the majority Democrats had been insisting on as a means of chipping away at the budget deficit rather than relying solely on cuts to social programs.
Presidential adviser David Plouffe, speaking on NBC's "Meet the Press," had again dismissed speculation Obama would invoke the 14th Amendment to force payment of debts if Congress fails to lift the ceiling by Tuesday.
The Reid plan would have raised the $14.3 trillion debt limit by up to $2.4 trillion in two stages -- $1 trillion now, matched by cuts, and the rest in 2012 unless two-thirds of both houses disapprove, The Washington Post said.
Without steering legislation, the United States will be unable to meet most of its financial obligations after Tuesday, The New York Times said.
McConnell said his package includes a vote on a balanced budget amendment to the Constitution before raising the debt ceiling but no requirement that it pass, as in the House Republican proposal.
Sen. John Thune, R-S,D., said on "Meet the Press": "This is probably going to be as good of an outcome as we can get, and most of us are going to have to accept things that we don't like in the final product."
Sen. Claire McCaskill, D-Mo., said: "Let's get away from the situation where the people who have power in Washington don't have to pay any taxes."
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