"It's time for Democrat leaders to take 'yes' for an answer," McConnell said in a statement.
The U.S. government has been partially shut since Oct. 1 because of Congress' failure to pass a normally routine temporary spending bill. Separately, Obama wants Congress to extend the government's borrowing authority another matter that usually had been routine.
The latest snag comes as 350,000 federal workers remain idle, hundreds of thousands more work without pay and an array of government services, from home loan applications to environmental inspections, remain on hold on the 13th day of the shutdown. Last week, the effects of the shutdown reached businesses, such as concessions and hotels near federal parks, that depend on government programs.
Many national parks and monuments remain closed, drawing a protest at the National World War II Memorial on Sunday that included tea party-backed conservative lawmakers who had unsuccessfully demanded defunding of Obama's 3-year-old signature health care law in exchange for keeping the government open.
Unnerving to world economies is the prospect of the United States defaulting on its financial obligations on Thursday if Congress fails to raise the borrowing authority above the $16.7 trillion debt limit.
Christine Lagarde, the International Monetary Fund's managing director, spoke fearfully about the disruption and uncertainty, warning of a "risk of tipping, yet again, into recession" after the fitful recovery from the 2008 global recession. The reaction of world financial markets and the Dow Jones on Monday will influence any congressional talks.
Congress is racing the clock to get a deal done, faced with time-consuming Senate procedures that could slow legislation, likely opposition from hardcore conservative tea party-backed lawmakers, and certain resistance in the Republican-led House of Representatives before a bill gets to Obama.
Politically, Republicans are reeling, bearing a substantial amount of the blame for the government shutdown and stalemate, according to recent polls..
"We're in a free-fall as Republicans, but Democrats are not far behind," said Republican Sen. Lindsey Graham, in warning Democrats about seizing on the Republicans' bruised brand as leverage to extract more concessions.
McConnell and Republicans want to continue current spending at $986.7 billion and leave untouched the new round of cuts in January, commonly known as the sequester, that would reduce the amount to $967 billion. Democrats want to figure out a way to undo the reductions, plus a long-term extension of the debt limit increase and a short-term spending bill to reopen the government.
Sen. Dick Durbin, the No. 2 Democrat in the Senate, told reporters that the two sides are roughly $70 billion apart, the difference between the $1.058 trillion Senate budget amount and the $988 billion envisioned by House Budget Committee Chairman Paul Ryan.
"We haven't picked a number, but clearly we need to negotiate between those two," Durbin said.
Republicans dismiss the latest request as Reid moving the goalposts in negotiations as they were getting closer to resolving the stalemate that has paralyzed Washington. They also argue that it is disingenuous for Democrats to resist any changes in the 3-year-old health care law while trying to undo the 2011 budget law that put the cuts on track.
Republican Sens. Lindsey Graham and Rand Paul said they would not support any deal that upends the spending limits imposed by the 2011 law, and predicted that their Senate Republican colleagues would oppose it as well.
The House of Representatives and its fractious Republicans remained a possible headache in the coming week.
Out of play for now was the House, where Speaker John Boehner told fellow Republican lawmakers early Saturday that his talks with the president had ground to a halt. Obama telephoned House Democratic leader Nancy Pelosi on Sunday, focusing on the need for any increase in the debt limit to be passed without concessions.
Also sidelined, at least for now, was the plan forged by Collins and a bipartisan coalition 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 announced Saturday it was going nowhere.
Collins was on CNN's "State of the Union." Graham appeared on ABC's "This Week," Schumer spoke on CBS' "Face the Nation" and Lagarde was on NBC's "Meet the Press."
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Associated Press writers Donna Cassata, David Espo, Kimberly Hefling and Michele Salcedo contributed to this report.
