Congressional Republicans are trying to figure out which card to play next after the White House got into some high-stakes poker-playing over the weekend, with Treasury Secretary Timothy Geithner effectively calling the GOP's bluff on the debt limit.

Republicans for weeks have threatened to withhold their support for raising the $14.3 trillion ceiling unless and until they see substantive commitments to cut spending and reform the budget. Washington is expected to hit that ceiling by next month. Even with the wiggle room Treasury might be able to create to extend the deadline, that doesn't leave lawmakers a lot of time to reach a deal.

But Geithner, speaking on two Sunday shows, said he's not worried. He said Congress will raise the debt limit and suggested leaders from both parties assured President Obama last week they won't let the country go into default.

"Congress is going to have to raise the debt limit. They understand that," Geithner said on NBC's "Meet the Press." He said the administration wants to figure out a long-term deficit-reduction plan while Congress takes up the debate over the debt limit; but if the government hits that ceiling before a deal is reached, the ceiling will have to be raised regardless.

"Congress will raise the debt ceiling," he said, in a separate interview on ABC's "This Week."

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But if Republicans offered the administration assurances in private, they certainly weren't doing so in public. House Speaker John Boehner has loudly threatened to extract concessions out of the administration in exchange for support on the debt ceiling.

Tea Party-aligned lawmakers suggested Sunday they were still serious about linking the debt vote to spending cuts.

"I don't think he's calling anyone's bluff," Sen. Mike Lee, R-Utah, told "Meet the Press." "What I'm focused on is not as much the debt limit, but what we do to make sure that we're not stuck in the same position again just a few months from now. We keep doing the same thing over and over again, and until we put a different kind of process in place, a structural spending reform, it's going to continue to happen."

Sen. Rand Paul, R-Ky., on CNN's "State of the Union," said it's "yet to be determined" whether he would support a filibuster on the debt ceiling vote.

Sen. Tom Coburn, R-Okla,, said on "Fox News Sunday" that he needs to have "absolute certainty" a deficit reduction plan includes "critical changes."

"Unless we do that, there's no way I'll support it," Coburn said on the debt ceiling increase. "We're going to have a debt crisis, either with this or soon thereafter, if we don't come together."

Rep. Chris Van Hollen, D-Md., though, said Congress should not "monkey around with the full faith and credit of the United States."

"Linking the two and saying you're only going to vote for the debt ceiling if something particular happens on deficit reduction I think is playing Russian roulette with, like, the fully loaded revolver," he said on "Fox News Sunday."

Geithner said repeatedly that lawmakers who want to take the country to the "brink" will bear the responsibility for the risk that creates.

He suggested that merely flirting with that edge would create a problem. But he said if Congress ultimately rejects an increase in the debt limit, it would trigger a crisis that makes that 2008 meltdown look tame. Geithner reiterated warnings that such a vote would force the government to halt benefits payments to seniors and veterans and would risk the government defaulting on its interest.