Under a proposal outlined by Sen. Mitch McConnell of Kentucky, Obama could request increases of up to $2.5 trillion in the government's borrowing authority in three separate installments over the next year, as long as he simultaneously proposed spending cuts of greater size.
The debt limit increases would take effect unless blocked by Congress under special rules that would require speedy action - and even then Obama could exercise his authority to veto such legislation. Significantly, the president's spending cuts would be debated under normal procedures, with no guarantee they ever come to a final vote.
In essence, McConnell's proposal would greatly enhance Obama's authority to avoid a default, while also virtually absolving Republicans of responsibility if one occurred.
At the same time, it would allow Republican lawmakers to avoid having to support an increase in the debt limit, something many of them find odious.
"Republicans will choose a path that actually reflects the will of the people, which is to do the responsible thing and ensure the government doesn't default on its obligations," McConnell said in a speech on the Senate floor. He also excoriated the administration for seeking tax increases along with spending cuts as part of an agreement to raise the debt limit.
His plan drew criticism from GOP presidential contender Newt Gingrich, who quickly tweeted it was "an irresponsible surrender to big government, big deficits and continued overspending."
There was no immediate response to the GOP proposal from the White House, where Obama hosted his third meeting in as many days with congressional leaders struggling to avert a financial crisis.
The talks have revolved around attempts to meet Republican demands for deficit cuts at least as large as any increase in the debt limit. Negotiators have grown testy in recent days as Obama and Democrats pushed for higher tax revenue as part of the deal, a line Republicans say they will not cross.
It was unclear whether McConnell's proposal could show the White House and congressional leaders of both parties a way out of a deadlock that Obama and others said threatened calamitous results for an economy still struggling to recover from the worst recession in decades.
It would obligate Obama to outline deep spending cuts, something Republicans have been trying to force him to do for months without much success.
Reductions as large as $2.5 trillion would almost certainly affect domestic programs seen as important by Democratic constituencies and by rank-and-file lawmakers, possibly including Medicare and Medicaid. Even if the cuts never took effect, Republicans would be able to call for votes, while identifying them as sponsored by the White House.
Any such proposals could also be used by Republicans in the 2012 campaigns, if only to blunt attacks made by Democrats.
The White House talks have been aimed at producing a compromise to cut projected deficits by trillions of dollars over the next decade while renewing the Treasury's authority to resume borrowing.
The government reached its current $14.3 trillion borrowing limit several weeks ago, and Treasury officials have been relying on accounting maneuvers to continue to pay the nation's bills without additional borrowing.
While Obama and Republicans maneuvered for political position, New York Mayor Michael Bloomberg said during the day that the two parties' debate over deficit reduction "should not be tied to the debt ceiling."
"America's good name and credit are just too important to be held hostage to Washington gridlock," he said in a speech a few miles away from the nation's financial center of Wall Street.
Bloomberg's concern echoed similar expressions by Obama and Treasury Secretary Timothy Geithner, and neither McConnell nor House Speaker John Boehner has disputed the assertion that a default could bring disaster to the economy that is growing so slowly that unemployment stands at 9.2 percent nationally.
Still, in remarks made before McConnell unveiled his proposal, Boehner said bluntly of the president, "This debt limit increase is his problem and I think it's time for him to lead by putting his plan on the table - something that the Congress can pass."
Boehner noted he had been telling the White House for months there are "no tax increases on the table" as part of the debt reduction talks.
In back-channel talks with the White House last week, officials say Boehner and Obama discussed the possibility of a huge $4 trillion deal in which Democrats accepted cuts in Medicare, Medicaid and perhaps Social Security and the GOP supported an end to certain tax breaks in anticipation of sweeping tax reform legislation before the elections.
But House Majority Leader Eric Cantor, R-Va., and other conservatives objected to White House demands for $1 trillion in new revenue. Boehner issued a statement Saturday backing away from the larger deal.
McConnell's Senate speech was particularly pointed when he spoke of Obama, whose defeat in 2012 he has called his top political priority.
"Rather than find a way to bring government back to the people, the administration has committed itself to protecting the size and scope of government at the cost of job creation, economy growth and America's status in the global economy," he said.
Under his proposal, the debt limit would rise by $100 billion as soon as Obama requested the first of the three increases envisioned.
Officials have said that the government normally borrows about $125 billion a month to finance operations, meaning Obama could avoid a default for a brief period of time simply by asking for it.
Associated Press writers Andrew Taylor, Laurie Kellman, Ben Feller, Julie Pace and Erica Werner contributed to this report.