Story highlights Senate Democrats hope McConnell will "cut through the clutter" of GOP positions

No agreements, but senators of both parties offer positive words

The President "rejected" House GOP proposal, Republican lawmaker says

House Republicans have been sidelined

Congressional negotiators had no agreements to report Saturday, but they issued positive reports on their talks to end a partial government shutdown and avert a default on government debt.

"Cordial" was the word Senate Majority Leader Harry Reid, D-Nevada, used to describe his "preliminary" discussions with Senate Republican Leader Mitch McConnell of Kentucky.

"Good" discussions were going on among Senate leaders, said Sen. Bob Corker, R-Tennessee, "so I think all of us want to support those efforts, and hopefully they bear fruit over the weekend."

For all the positive talk, the only actions Saturday fell into the "no" category:

--Republican leaders said President Barack Obama rejected their proposal for a six-week debt limit extension.

--The Senate defeated a procedural measure to extend the debt limit with no strings attached.

--Reid said a proposal by a bipartisan group of senators, led by Republican Sen. Susan Collins of Maine, is no longer on the table because it treated opening the government as a "concession."

Reid continues to demand that any plan include a "clean" bill with no strings attached that raises the debt limit and reopens the government.

Countdown to default

The Treasury Department says it will be unable to pay the government's bills unless the debt limit is increased by Thursday. The partial shutdown of government services has been in effect since October 1.

Christine Lagarde, head of the International Monetary Fund, said Saturday the consequences of a failure to raise the debt limit would be dire for economies around the world. She spoke to CNN's Richard Quest at an Institute of International Finance conference in Washington.

"You know, I've just spent the last two days with representatives of about 188 countries around the world. I wouldn't say they are confident. I would say they are concerned, and they are very anxious to see this crisis resolved, because they know it's going to impact on their economy," Lagarde said.

Senate Democrats meet with president

Senate Democrats met with Obama for 75 minutes Saturday afternoon. A Senate Democratic leadership aide said the party is unified.

"Democrats are willing to negotiate on anything Republicans want to discuss as soon as we reopen the government and pay our bills," said the aide.

Another Democratic source said party leaders regard Republicans as lacking a coherent position. They hope McConnell can "cut through the clutter," the source told CNN's Dana Bash.

The sources, who are familiar with the talks, spoke on the condition of anonymity so they could speak candidly.

Despite the lack of agreement, Sen. Chuck Schumer, D-New York, said progress was being made.

"I think our Republican colleagues are moving in our direction with the fact that Obamacare is not a major part of the discussion anymore among most all Senate and many House Republicans," he said.

No votes on Sunday

Before the White House meeting, the Senate's second highest-ranking Democrat, Richard Durbin of Illinois, told CNN's Deirdre Walsh that Democrats hoped to reach agreement with Republican negotiators before stock markets open Monday.

Even if that optimistic timetable could be met, a deal could not be voted upon Sunday.

The Senate is scheduled to come back into session at 1 p.m. ET Sunday, but no votes are planned and Senators have been told their presence is not required. The House is not scheduled to meet until Monday afternoon.

Even as he demanded a "clean" bill, Reid said it was encouraging that McConnell had approached him to start their weekend talks.

"I hope that our talking is some solace to the American people and the world," Reid said. He said McConnell had approached him. "This hasn't happened until now," Reid said.

Obama-Boehner talks stall

Republican leadership told the Republican caucus during a Saturday morning meeting that the president will not accept their proposal to raise the debt limit for six weeks.

Rep. Raul Labrador, R-Idaho, told CNN Saturday that "the President rejected our deal."

The standstill came after a Friday afternoon phone call between Boehner and Obama in which they decided to keep talking.

Rep. Adam Kinzinger, R-Illinois, said the President is waiting for a better offer.

"It doesn't seem like the White House is serious at all about entering negotiations with us until they see what comes out of the Senate. If they get something out of the Senate that's weaker than our negotiated position, it obviously strengthens their position," Kinzinger said.

While Democrats flat out rejected Boehner's proposal, even some Republicans didn't like it. That's because it lacked a mechanism in the House proposal to immediately reopen the government, which has been partially shut down since October 1, prompting the furlough of hundreds of thousands of workers, the closing of national parks and an increase in public anger.