"I think we're in a position where we'll be able to get well above $1 trillion pretty quick in terms of what would be a down payment on the process," Biden said after a three-hour meeting on Capitol Hill with top lawmakers.

Republicans have said that any deal to raise the debt limit would have to include spending cuts of equal size.

A $1 trillion "down payment" could allow Congress to back a debt-limit increase which would cover the country's borrowing needs roughly through February 2012.

That would require Congress to revisit the politically painful issue before the November 2012 elections.

Democrats and Republicans agree that the United States needs to reduce budget deficits by $4 trillion over the coming decade to ensure its debt remains at a manageable level.

Negotiators are considering deficit-reduction targets that would trigger automatic spending cuts and perhaps tax increases if they are not reached in coming years.

That would give them more time to resolve stubborn disputes over taxes and costly federal healthcare programs that have derailed other bipartisan deficit-reduction efforts.

Biden reiterated the Democratic position that any deficit-reduction deal would need to include tax increases.

It was unclear whether the $1 trillion would consist of spending cuts alone, as Republicans insist.

In their third round of talks, the group examined the Medicare and Medicaid government health plans for retirees and the poor, which represent nearly a quarter of all federal spending and are expected to eat up a growing portion of the budget in coming decades as the population ages and medical costs continue to outstrip inflation.

President Barack Obama and Republicans hope to slow the growth of the two programs, but they are deeply divided about how to do so and their plans differ by $1.86 trillion.

Finding common ground will be difficult as the election season heats up.

Polls show that a Republican plan to scale back Medicare for future retirees is unpopular with the public and Democrats see an opportunity to pick up votes by campaigning against it.

Democrats are hoping for victory later on Tuesday in a special U.S. House of Representatives election in a Republican-leaning district in upstate New York, where Medicare's future has been a major issue.

Adding to the pressure, Senate Democrats plan a vote this week on the plan, which has already passed the House, in order to force their Republican colleagues to take a stand on it.

Some Republicans say Biden's talks are laying vital groundwork for an eventual compromise on measures to ensure that the national debt remains at a sustainable level, but that Obama will ultimately be required to seal the deal.

The group, which is next scheduled to meet on Thursday, had already found about $150 billion in cuts in areas like farm subsidies and federal employee retirement benefits.

On healthcare, both sides have suggested changes to the way in which the federal and state governments administer Medicaid.

The Treasury Department is tapping pension funds and other pots of money now that the country has reached its debt limit, but has warned that it will exhaust those measures by Aug.2.

Failure to increase the debt limit by then could force the United States to miss interest payments on its debt, which could push the country back into recession and rattle markets across the globe.

However, a new poll by Pew Research Center found that Americans are more concerned about increased government spending than they are about a debt default.