The agreement would reduce federal spending by at least $2.2 trillion over a decade, a steep price for many Democrats and too little for many Republicans.
No votes were expected in either house of Congress until Monday at the earliest, to give rank-and-file lawmakers time to review the package. Senate approval appears to be certain; the House could prove more difficult.
In an address from the White House, Obama said the agreement "will allow us to avoid default and end the crisis that Washington imposed on the rest of America."
Default "would have had a devastating effect on our economy," the president said. The resolution instantly powered a rise in financial markets overseas.
The Treasury's authority to borrow would be extended beyond the 2012 elections, a key objective for Obama, though the president had to give up his insistence on raising taxes on wealthy Americans to reduce deficits.
"It isn't the greatest deal in the world, but it shows how much we've changed the terms of the debate in this town," House Speaker John Boehner said on a conference call, according to GOP officials. Boehner added that the agreement was "all spending cuts. The White House bid to raise taxes has been shut down."
Without legislation in place by Tuesday, the Treasury would not be able to pay all its bills, raising the threat of a default that administration officials say could inflict catastrophic damage on the economy.
If approved, a compromise would presumably preserve America's sterling credit rating, reassure investors in financial markets across the globe and possibly reverse the losses that spread across Wall Street in recent days as the threat of a default grew.
The Associated Press contributed to this report.