Sen. Ted Cruz, R-Texas, a force in pushing Republicans to link changes to the health care law in exchange for keeping the government running, spelled out his conditions for raising the borrowing authority.
"We should look for three things. No. 1, we should look for some significant structural plan to reduce government spending. No. 2, we should avoid new taxes. And No. 3, we should look for ways to mitigate the harms from 'Obamacare,'" Cruz said, describing the debt ceiling issue as one of the "best leverage the Congress has to rein in the executive."
Some Republicans, such as Rep. Steve King of Iowa, dismiss the warnings about a government default as an exaggeration, suggesting U.S. credit won't collapse and calling the talk "a lot of false demagoguery."
Asked how the standoff might end, Boehner said Sunday on ABC that he was uncertain: "If I knew, I'd tell you."
The Ohio Republican added that Obama can call him any time to start negotiations to end the shutdown. "He knows what my phone number is," Boehner said.
Privately, administration officials say they don't think Boehner and Senate Republican leader Mitch McConnell want a default as they realize it will be far worse than a shutdown, but the two don't know how to avoid it or when to try.
In one promising development, a large chunk of the furloughed federal work force is headed back to the Pentagon on Monday, and those who remain at home or are working without paychecks are a step closer to getting back pay once the partial government shutdown ends.
Defense Secretary Chuck Hagel ended the argument for most Pentagon civilian employees, ordering nearly all 350,000 back on the job. Hagel said he based his decision on a Pentagon interpretation of a law called the Pay Our Military Act.
The Senate will try to vote this week on a bill that passed the House unanimously on Saturday to pay federal workers for days missed.
Boehner and Schumer were interviewed on ABC's "This Week," and Lew and Cruz on CNN's "State of the Union." Lew also appeared on CBS' "Face the Nation," ''Fox News Sunday" and NBC's "Meet the Press."