Among congressional leaders, however, animosity marked the stalemate and resolution seemed elusive.
A statement from Senate Majority Leader Harry Reid, D-Nev., accused Boehner of a credibility problem and called on him to allow a vote on a straightforward bill to re-open the government.
"There is now a consistent pattern of Speaker Boehner saying things that fly in the face of the facts or stand at odds with his past actions," said Adam Jentleson, a spokesman for Reid. "Americans across the country are suffering because Speaker Boehner refuses to come to grips with reality."
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In response, Michael Steel, a spokesman for Boehner, said it was "time for Senate Democrats to stow their faux outrage and deal with the problems at hand. The federal government is shut down because Democrats refuse to negotiate, and the debt limit is right around the corner."
Boehner said Sunday that he lacks the votes "to pass a clean CR," or continuing resolution, a reference to the temporary spending bill without conditions that would keep the government operating.
Lew has warned that the budget brinkmanship was "playing with fire" and implored Congress to pass legislation to re-open the government and increase the nation's debt limit.
The shutdown has pushed hundreds of thousands of workers off the job, closed national parks and museums and stopped an array of government services.
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The one bright spot on Monday is a significant chunk of the furloughed federal workforce is headed back to work. Defense Secretary Chuck Hagel ordered nearly 350,000 back on the job, basing his decision on a Pentagon interpretation of a law called the Pay Our Military Act.
Democrats insist that Republicans could easily open the government if Boehner simply allows a vote on the emergency spending bill. Democrats argue that their 200 members in the House plus close to two dozen pragmatic Republicans would back a so-called clean bill, but the speaker remains hamstrung by his tea party-strong GOP caucus.
"Let me issue him a friendly challenge. Put it on the floor Monday or Tuesday. I would bet there are the votes to pass it," said Sen. Chuck Schumer, D-N.Y.
In a series of Sunday television appearances, Lew said that while Treasury expects to have $30 billion of cash on hand on Oct. 17, that money will be quickly exhausted in paying incoming bills given that the government's payments can run up to $60 billion on a single day.
Treasury issued a report on Thursday detailing in stark terms what could happen if the government actually defaulted on its obligations to service the national debt, with credit markets frozen, the dollar in free fall and U.S. interest rates skyrocketing.
—By The Associated Press.