Leaders of both parties in the U.S. Congress are reported to be engaged in a major effort to work out compromise legislation that will keep the government from defaulting on its $14.3 trillion debt.

On Sunday, the Senate voted to block consideration of a proposal to raise the federal government’s borrowing authority put forward by Harry Reid, the leader of the Democratic Party in the Senate. But the outcome did not stand in the way of negotiations involving the White House and congressional leaders aimed at an ending the weeks-long deadlock.

There have been expressions of optimism on both sides that an agreement can be reached before Tuesday, considered the deadline for Congress to increase the debt limit and prevent the federal government from defaulting on its debts.

The Republican leader in the Senate, Mitch McConnell, told reporters Sunday, “I think we’ve got a chance of getting there” on a deal to increase the debt limit while cutting government spending. A White House official was quoted as saying a deal was “not there yet.”

There is concern in financial markets over a possible U.S. government default that would threaten an already fragile economy. Last week U.S. stock markets suffered their worst losses this year, and the value of the dollar slumped.

Past increases in the debt limit have been routine, but Republicans in Congress have demanded huge spending cuts with no increase in taxes as a condition for approving an increase this time.

Republicans had been calling for an immediate short-term agreement and a revisiting of the debt ceiling debate next year, while Democrats were pushing for a plan to cover the nation’s borrowing needs past the presidential and congressional elections in November 2012.