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Washington (CNN) -- The framework of a tentative deal to raise the nation's debt ceiling calls for up to $2.8 trillion in total deficit reduction over the next decade, two sources familiar with the negotiations told CNN late Saturday night.

The agreement, still being negotiated by the White House and bipartisan congressional leaders, would allow the debt ceiling to be raised by enough to last at least through the end of 2012.

The debt limit would be increased in two stages, both of which would occur automatically -- a key Democratic demand that would prevent a repeat of the current crisis before the next election.

The agreement includes upfront spending cuts in the range of roughly $1 trillion, the sources said. A special congressional committee would recommend additional spending reductions of up to $1.8 trillion no later than Thanksgiving. If Congress failed to approve the recommended cuts by late December, automatic, across-the-board cuts -- including both defense and Medicare -- would take effect.

News of a possible deal came shortly after the Senate delayed consideration of Majority Leader Harry Reid's debt ceiling proposal late Saturday night, pushing back a key procedural vote by 12 hours.

The vote to stop debate and end a GOP filibuster on the plan will now be held at 1 p.m. ET on Sunday, as opposed to 1 a.m.

Reid, D-Nevada, said he was asking for a delay to provide additional time for negotiations underway at the White House.

There are "many elements to be finalized" and still "a distance to go," Reid said. "We should give everyone as much room as possible to do their work."

Reid's announcement capped a day of sharp partisan voting in the House and extended talks behind closed doors between congressional and administration officials. Concern continued to grow that Congress will fail to raise the nation's debt ceiling in time to avoid a potentially devastating national default next week.

Earlier in the day, the Republican-controlled House rejected Reid's plan -- partisan payback for the Democratic-controlled Senate's rejection of GOP House Speaker John Boehner's plan Friday night.

House members rejected Reid's plan in a 173-246 vote. Most Democrats supported the measure; every Republican voted against it.

Forty-three of the Senate's 47 Republicans, meanwhile, sent a letter to Reid promising to oppose his plan as currently drafted. Maine's Olympia Snowe and Susan Collins, Massachusetts' Scott Brown, and Alaska's Lisa Murkowski declined to sign it.

Regardless, Democrats plowed ahead with the talks in the hope that modifications could be made to win over at least seven Senate Republicans and reach the 60-vote threshold required to clear the measure through the Senate and ultimately the House.

Senate Minority Leader Mitch McConnell, R-Kentucky, spoke with Vice President Joe Biden several times Saturday, according to a senior administration official. Reid and House Minority Leader Nancy Pelosi, D-California, met with Obama at the White House.

As the day wore on, Democratic and Republican leaders appeared at odds over whether any progress was being made toward a final agreement. At one point, both Boehner, R-Ohio, and McConnell declared that a deal was close -- an assertion which prompted Reid to take to the Senate floor and insist that the claim was the simply "not true."

The Republicans are holding "meaningless press conferences" and "refuse to negotiate in good faith," Reid said. "The process has not been moved forward during this day."

"I'm more optimistic than my friend the majority leader," McConnell replied. "I think we've got a chance of getting there."

One Democratic source cited concern among congressional Democrats that Obama could be close to cutting a deal with Republicans at their expense.

While the political maneuvering continued, the clock continued to tick down. If Congress fails to raise the current $14.3 trillion debt ceiling by August 2, Americans could face rising interest rates and a declining dollar, among other problems.

Some financial experts have warned of a downgrade of America's triple-A credit rating and a potential stock market plunge. The Dow Jones Industrial Average dropped for a sixth straight day on Friday.

Without an increase in the debt limit, the federal government will not be able to pay all its bills next month. Obama recently indicated he can't guarantee Social Security checks will be mailed out on time.

For their part, Republicans continued to trumpet Boehner's proposal. The measure cleared the House Friday, but only after a one-day delay during which the speaker was forced to round up support from wary tea party conservatives. Boehner's deal with conservatives -- adding a provision requiring congressional approval of a balanced budget amendment to the Constitution in order to raise the debt limit next year -- was sharply criticized by Democrats, who called it a political nonstarter.

Boehner's "gone to the dark side," Pelosi said Saturday. "Let's go from the dark side to the bright side."

Democratic leaders vehemently object not only to the balanced budget amendment, but also the GOP's insistence that a second debt ceiling vote be held before the next election. They argue that reaching bipartisan agreement on another debt ceiling hike during an election year could be nearly impossible, and that short-term extensions of the limit could further destabilize the economy.

Obama urged compromise Friday, and asked Senate Democrats and Republicans on Friday to take the lead in the congressional deliberations.

"This is not a situation where the two parties are miles apart," the president insisted. But "we are almost out of time."

Leaders of both parties now agree that any deal to raise the debt ceiling should include long-term spending reductions to help control spiraling deficits. But they have differed on both the timetable and requirements tied to certain cuts.

Both the Reid and Boehner plans suffered setbacks earlier this week when the nonpartisan Congressional Budget Office released reports concluding that they fell short of their stated deficit reduction goals.

Boehner's plan, which has since been revised, proposed generating a total of $917 billion in savings while initially raising the debt ceiling by $900 billion. The speaker has pledged to match any debt ceiling hike with dollar-for-dollar spending cuts.

His plan, however, would require a second vote by Congress to raise the debt ceiling by a combined $2.5 trillion -- enough to last through the end of 2012. It would create a special congressional committee to recommend additional savings of $1.6 trillion or more.

Any failure on the part of Congress to enact mandated spending reductions or abide by new spending caps would trigger automatic across-the-board budget cuts.

The plan, as amended Friday, also calls for congressional passage of a balanced budget amendment before the second vote to raise the debt ceiling, which would likely be required at some point during the winter.

As for Reid's plan, a revised version he proposed Friday would reduce deficits over the next decade by $2.4 trillion and raise the debt ceiling by a similar amount. It includes $1 trillion in savings based on the planned U.S. withdrawals from military engagements in Afghanistan and Iraq.

Reid's plan also would establish a congressional committee made up of 12 House and Senate members to consider additional options for debt reduction. The committee's proposals would be guaranteed by a Senate vote with no amendments by the end of the year.

In addition, it incorporates a process based on a proposal by McConnell that would give Obama the authority to raise the debt ceiling in two steps while providing Congress the opportunity to vote its disapproval.

Among other things, Reid has stressed that his plan meets the key GOP demand for no additional taxes. Boehner, however, argued this week that Reid's plan fails to tackle popular entitlement programs such as Medicare, which are among the biggest drivers of the debt.

A recent CNN/ORC International Poll reveals a growing public exasperation and demand for compromise. Sixty-four percent of respondents to a July 18-20 survey preferred a deal with a mix of spending cuts and tax increases. Only 34% preferred a debt reduction plan based solely on spending reductions.

According to the poll, the public is sharply divided along partisan lines; Democrats and independents are open to a number of different approaches because they think a failure to raise the debt ceiling would cause a major crisis for the country. Republicans, however, draw the line at tax increases, and a narrow majority of them oppose raising the debt ceiling under any circumstances.

CNN's Ted Barrett, Kate Bolduan, Gloria Borger, Keating Holland, Brianna Keilar, Jeanne Sahadi, Xuan Thai, Jessica Yellin, Barbara Starr and Deirdre Walsh contributed to this report.