The US Treasury Department has warned it will run out of money to cover the country's bills if Congress does not increase its borrowing authority by 2 August.
Treasury Secretary Timothy Geitner has warned of catastrophic damage to the global economy if Congress fails to agree a deal soon.
President Barack Obama and top lawmakers failed to achieve a breakthrough in a roughly 90-minute meeting and scheduled a third straight day of talks for Tuesday.
Mr Obama discussed with the lawmakers a deficit-reduction plan negotiated by a group led by Vice President Joe Biden. The plan had included up to $US2 trillion in spending cuts but fell apart over Democratic demands that it include an end to $400 billion in tax loopholes.
Democrats familiar with the White House talks said that in the meeting, Democratic lawmakers indicated there would not be votes from their side for a deficit-reduction bill that only had spending cuts, as Republicans want.