Washington (CNN) -- Thirteen days into a partial government shutdown, four days before the U.S. government bumps up against its projected borrowing limit, and there was little sign of movement toward resolving the latest budget impasse Sunday.
Speaking on CNN's "State of the Union," a bipartisan pair of senators expressed hope that they and other members of the chamber could work out a plan acceptable to both sides.
"It's taken far too long. We never should be in this situation," said Sen. Susan Collins, R-Maine. "But I do believe there's going to be a resolution this week."
Collins and Sen. Amy Klobuchar, D-Minnesota, said more than a dozen senators have been involved in their effort calling for a longer extension of the debt limit and government funding.
"We had 12 people meet yesterday, but just last night I had two more Democrats and a Republican contact me to offer suggestions and say they want to be part of our group," Collins said.
And on NBC's "Meet the Press," the Senate's No. 2 Democrat, Illinois Sen. Dick Durbin, said there had been a "breakthrough" over the weekend, with the GOP leadership of the House of Representatives stepping aside and leaving negotiations to the Senate.
But while reports of talks were positive, the only actions over the weekend involved one "no" after another.
-- Senate Majority Leader Harry Reid said Saturday that the plan Collins was assembling is no longer on the table, because it treated reopening the government as a "concession." Reid continues to demand that any plan include a "clean" bill, one that raises the debt limit and reopens the government with no strings attached.
-- Republicans blocked a measure to extend the debt limit with no strings attached, refusing to support a procedural vote that would have brought it to the Senate floor.
-- House Republican leaders said President Barack Obama rejected their proposal for a six-week extension of the federal debt ceiling.
"There was some movement a couple of days ago, and I think things are not moving now," Sen. Bob Corker, R-Tennessee, told "Fox News Sunday."
"I do think we will see our way through this, but the last 24 hours have not been good," he added.
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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.
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.
Senate Democrats met with Obama for 75 minutes Saturday afternoon, and 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 Senate Minority Leader Mitch 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.
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Even as he demanded a "clean" bill, Reid said he and McConnell are involved in "cordial" and "preliminary" discussions.
"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.
The House GOP leadership told Republicans during a Saturday morning meeting that Obama will not accept their proposal to raise the debt limit for six weeks.
Rep. Raul Labrador, R-Idaho, told CNN on Saturday that "the President rejected our deal."
The standstill came after a Friday afternoon phone call between House Speaker John Boehner and Obama in which they decided to keep talking.
Rep. Adam Kinzinger, R-Illinois, said Obama 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. The shutdown has led to the furlough of hundreds of thousands of workers, the closing of national parks. and an increase in public anger.