Congressional Republicans, who only last week had been threatening to close down the federal government, emerged from closed-door negotiations at a party retreat to announce they will present a bill next week to increase the debt limit by a further three months.
The White House gave the move a cautious welcome to the news.
It is an unexpected bonus for Obama just days before the start of his second presidential term, and gives him breathing space so that instead of another showdown between White House and Republicans in Congress at the end of next month or in March, the issue could be pushed back until summer.
Eric Cantor, the Republican majority leader in the House, said: "Next week, we will authorise a three-month temporary debt limit increase to give the Senate and House time to pass a budget."
The GOP came close to closing down the federal government in 2011 when they initially refused to raise the debt ceiling.
A messy compromise was eventually worked out. But Obama said earlier this month, after yet another economic showdown, he would not negotiate with the Republicans over the debt limit.
Obama, ramping up pressure on opponents in Congress, held a press conference at the White House on Monday, warning them that if they were not prepared to raise the ceiling, then they would have to take the blame for government closing down.
Obama's strategy appears to have worked, with the Republicans worried about the electoral consequences of government grinding to a halt, which would mean hundreds of thousands of people – from welfare recipients to veterans – no longer receiving their cheques, federal staff going on forced leave and agency after agency being shut down.
The Republican cave-in was announced from their retreat near Colonial Williamsburg, Virginia, where they have been discussing overall strategy in the wake of the November elections.
In what appears to be a political gimmick, the Republicans are to attach to the bill extending the debt limit for three months clauses that would see members of Congress have their pay withheld unless they can reach agreement on a separate issue: a budget that cuts spending.
The Republicans had been using the debt ceiling crisis as leverage to try to force Obama into accepting deep spending cuts, particularly in welfare.
Cantor, in a statement, said of the proviso in next week's bill about the three-month extension: "If the Senate or House fails to pass a budget in that time, members of Congress will not be paid by the American people for failing to do their job. No budget, no pay."
The Republicans are banking on the idea of members' losing their pay being popular with voters.
But both the White House and the Democratic leadership in the Senate dismissed the idea, saying they wanted a "clean bill", focused solely on raising the debt ceiling.
The White House, in a statement, said: "The president has made clear that Congress has only two options: pay the bills they have racked up, or fail to do so and put our nation into default.
"We are encouraged that there are signs that congressional Republicans may back off their insistence on holding our economy hostage to extract drastic cuts in Medicare, education and programs middle class families depend on. Congress must pay its bills and pass a clean debt limit increase without further delay. And as he has said, the president remains committed to further reducing the deficit in a balanced way."
The Democratic leader in the Senate, Harry Reid, said if the House passes a clean bill raising the debt ceiling, even temporarily, the Senate would be happy to consider it.
A spokesman said Reid saw the move as the Republicans beginning to back off from their threat to "hold our economy hostage".
Separate from the debt ceiling, a deal on spending is within reach. Obama has already agreed to consider changes to the index that determines welfare benefits, something the Republicans have been pushing for but Democrats have resisted, and to raise the age at which Medicare kicks in, another Republican proposal.
He and the Republican House speaker, John Boehner, are not too far apart either over a global figure for spending cuts.
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