According to a source familiar with the negotiations, what was believed to be a tentative deal would have included a debt ceiling increase of up to $2.8 trillion and spending cuts of about $1 trillion.
Sources said that was one of many being considered.
The deal may not please congressional Democrats or tea partiers.
Earlier Saturday, after weeks of intense partisanship, the White House and congressional leaders made a desperate, last-minute stab at compromise.
"There are many elements to be finalized...there is still a distance to go," Majority Leader Harry Reid cautioned in dramatic late-night remarks on the Senate floor.
Still, his disclosure that "talks are going on at the White House now," coupled with his announcement that progress had been made, offered the strongest indication yet that an economy-crippling default might be averted.
There was no immediate reaction from Senate Republican leader Mitch McConnell or House Speaker John Boehner, President Barack Obama's principal Republican antagonist in a contentious era of divided government.
Reid said that at the request of White House officials, he was postponing a test vote set for shortly after midnight on his own legislation to raise the debt limit while cutting spending.
Republicans opposed his bill, and said in advance they had the votes to block its advance.
Earlier in the day, McConnell said at a news conference with House Speaker John Boehner that they were "fully engaged...with the one person in America out of 307 million people who can sign a bill into law."
"I'm confident and optimistic that we're going to get an agreement in the very near future and resolve this crisis in the best interests of the American people," he said.
Without legislation in place by next Tuesday, administration officials say the Treasury will run out of funds to pay all the nation's bills. They say a subsequent default could prove catastrophic for the U.S. economy and send shockwaves around the world.
The president is seeking legislation to raise the government's $14.3 trillion debt limit by about $2.4 trillion, enough to tide the Treasury over until after the 2012 elections. Over many weeks, he has agreed to Republican demands that deficits be cut - without a requirement for tax increases - in exchange for additional U.S. borrowing authority.
But Obama has threatened to veto any legislation that would require a second vote in Congress for any additional borrowing authority to take effect, saying that would invite a recurrence of the current crisis in the heat of next year's election campaigns.
The Associated Press contributed to this report.