WASHINGTON — Racing the calendar and the financial markets, Senate leaders have taken the helm in the search for a deal to end the partial government shutdown and avert a federal default.

"This should be seen as something very positive, even though we don't have anything done yet, and long ways to go," Senate Majority Leader Harry Reid, D-Nev., said Saturday, describing his opening conversation hours earlier with Senate Minority Leader Mitch McConnell, R-Ky.

"The real conversation that matters now is the one taking place between McConnell and Reid," said Sen. Bob Corker, R-Tenn.

Sens. Chuck Schumer, D-N.Y., and Lamar Alexander, R-Tenn., were also involved in the high-level bargaining.

Sunday marked the 13th day of a federal shutdown that has continued to idle 350,000 government workers, left hundreds of thousands of others working without pay and curtailed everything from veterans' services to environmental inspections.

More ominously, Thursday drew another day closer, the day the Obama administration has warned the U.S. will deplete its borrowing authority and risk an unprecedented federal default. Economists say that could send shockwaves throughout the U.S. and global economies.

The pressure was on both parties but seemed mostly on Republicans, who polls show are bearing the brunt of voters' wrath over the twin standoffs. And though the financial markets rebounded strongly late last week on word of movement in the talks, lawmakers of both parties were warily awaiting their reopening this week.

No. 2 Senate Democratic leader Dick Durbin of Illinois said the financial markets did better last week because they assumed that "eventually the damsel will be plucked from the tracks."

Referring to the approach of Thursday's deadline, he added: "As we start hearing the train whistle, I think that there may be a different view. I don't want to see it happen because it's going to hurt a lot of innocent people."

Republicans are demanding spending cuts and deficit reduction in exchange for reopening the government and extending its borrowing authority. President Barack Obama and other Democrats say they want both measures pushed through Congress without condition and would agree to deficit reduction talks afterward.

Out of play, for now, was the Republican-led House, where Speaker John Boehner, R-Ohio, told GOP lawmakers early Saturday that his talks with the president had ground to a halt.

Though the Senate was leading the search for a deal, the House and its fractious Republicans remained a possible headache in the coming week.

"At the end of the day, whatever they do still has to come through here," said Rep. Tom Cole, R-Okla., who is close to House leaders.

Also sidelined, at least for now, was an effort by Sen. Susan Collins, R-Maine, to assemble a bipartisan coalition for a plan to briefly fund the government and extend the $16.7 trillion debt limit, in exchange for steps like temporarily delaying the medical device tax that helps fund the health care law.

Democrats said Collins' plan curbed spending too tightly and Reid said it was going nowhere. Collins said she would continue seeking support for it.

Senate Republicans dealt Democrats an expected setback on Saturday by derailing a Democratic measure extending the debt limit through 2014 without any conditions. The vote was 53-45 to start debating the Democratic measure — seven short of the 60 votes needed to overcome GOP obstruction tactics.

AP Special Correspondent David Espo contributed to this report.