Senior Obama adviser David Plouffe indicated on NBC television there was an emerging consensus but no solid agreement yet.
"We don't have a deal," Plouffe said on NBC, stressing: "We have to get this solved. Today is obviously a critical day."
Business and finance leaders have warned default would send crippling aftershocks through the fragile US economy, still wrestling with stubbornly high unemployment of 9.2 per cent in the wake of the 2008 global meltdown.
Without a deal, the US government would have to cut an estimated 40 cents out of every dollar it spends, forcing grim choices between defaulting or cutting back programs like those that help the poor, disabled and elderly.
Any compromise would still need to clear the divided Democratic-led Senate and Republican-held House of Representatives, where conservatives close to the "Tea Party" movement have called for draconian belt-tightening.
In a partisan vote, the Senate Sunday voted against ending debate on a bill forwarded by Reid which remains in play and which could be used as a vehicle for a compromise.
Reid said a new tentative framework for an agreement would lift the debt limit beyond the November 2012 elections in which President Barack Obama seeks a second term, a key White House demand.
Aides familiar with the fast-moving negotiations said the two sides are close to an agreement to raise the debt ceiling by about $2.8 trillion, roughly what Obama asked for, in two stages.
"What's we're looking at is a $3 trillion package," McConnell told CNN.
That increase would come in two steps: A first tranche would cover roughly $1 trillion, paired with an equivalent number of spending cuts over 10 years.
"I think that what's clear is that pretty much both parties agree that there's going to be a first stage of deficit reduction, over a trillion dollars," Plouffe told ABC television.
The accord would create a special US Congress committee made up of an even number of Republicans and Democrats, due to recommend by late November 10-year deficit cuts equivalent to the second slice of debt-ceiling increase.
The two sides were still at odds over whether the committee could recommend an increase in tax revenues _ something Republicans fiercely oppose and would be able to block if their committee members held together.
"We're not going to raise taxes in this deal," said McConnell.
"I'm confident that any solution that this committee would produce, that ultimately will be voted on in Congress, is going to be balanced," said Plouffe, using the White House's term for a blend of cuts and tax revenue increases.
Much of the fighting focused on a punitive enforcement mechanism to avoid deadlock in an evenly split committee and failure to recommend new deficit-cutting measures.
Aides floated the possibility such a breakdown would trigger across-the-board spending cuts, or cuts to defence programs or the Medicare health program for elderly, while some Democrats pushed for tax revenue increases.
"You want something to compel this committee to act," insisted Plouffe.
AFP