Treasury Secretary Timothy Geithner boldly predicted that Congress will vote to raise the debt ceiling next month, warning that failure to do so would bring "catastrophic" consequences for the U.S. and global economies.

Geithner, appearing on ABC's "This Week," said that if House Republicans were to push the vote to the brink or fail to raise the limit, it would "make the last [financial] crisis look like a tame, modest crisis."

Geithner said that Republicans have told President Obama they "recognize we have to do this, and we're not going to play around with it."

"There's no alternative, and they recognize that," Geithner said.

Geithner said the Republican leadership assured Obama in a meeting at the White House on Wednesday that it understands the gravity of the debt-ceiling situation and will vote to raise it.

"The responsible people up there understand that," Geithner said.

But Republicans appearing on the Sunday talk shows demonstrated how tough a fight the White House might be facing just weeks after a near-shutdown of the government spurred by debates over fiscal 2011 spending.

House Budget Committee Chairman Paul RyanPaul Davis RyanSpending deal talks down to toughest issues, lawmakers say Schiff: I thought more Republicans would speak out against Trump Dem leaders pull back from hard-line immigration demand MORE (R-Wis.) said on CBS's "Face the Nation" that he has not been informed of any communication from House GOP leaders that they will back a raising of the debt ceiling no matter what.

Ryan said that, as he understands it, GOP leaders have told the White House: “In addition to raising the debt limit, we want financial controls, we want cuts in spending accompanying the raising of the debt ceiling.”

Sen. Tom CoburnThomas (Tom) Allen CoburnPaul Ryan should realize that federal earmarks are the currency of cronyism Republicans in Congress shouldn't try to bring back earmarks Republicans should know reviving earmarks is a political nightmare MORE (R-Okla.), a member of the Senate Gang of Six negotiations, and Rep. Chris Van Hollen (D-Md.), newly named to the Biden budget talks by House Minority Leader Nancy Pelosi (D-Calif.), previewed the battle to come, with Coburn making clear that he and other Republicans will not vote to raise the debt ceiling without an agreement on cuts.

Coburn made plain that he will not accept an increase in the nation's $14.3 trillion debt limit in the coming weeks without agreement on a debt-reduction package.

“What do I need? I need absolute certainty that we've made the critical changes that are necessary to put this country back where it needs to go. And unless we do that, there is no way I support it,” he said.

“We are going to have a debt crisis ... if we don't come together, so it's time to come together,” he said.

Van Hollen, the ranking member of the Budget Committee, said President Obama has laid out a “two-track” process whereby a "clean" debt-ceiling bill is passed and a deficit package is developed separately.

Freshman Sen. Rand PaulRandal (Rand) Howard PaulTrump informally offered Cohn CIA job before changing his mind: report Congress moving to end US involvement in Yemen Congress races to finish .2 trillion funding bill MORE (R-Ky.) said on CNN's "State of the Union" that he is unsure of how he will vote on raising the debt limit or whether he might filibuster an attempt to do so.

"I think we haven't yet determined what our strategy is going to be," the Tea Party favorite said, "but I can tell you that the people of Kentucky elected me to shake things up."

Geithner said that failing to raise the debt limit would result first in the U.S. stopping payments and benefits to seniors and veterans before risking default on interest loans. 

Default, Geithner said, would have a "permanent devastating effect" on the nation's credit-worthiness. 

"No responsible person" would play politics with the debt ceiling, Geithner said.

The White House has sent mixed signals about what Obama will accept in the debt-ceiling debate.

From the beginning, White House officials made a push for a "clean" bill raising the ceiling, but Obama has suggested in recent days that he would be open to coupling the debt ceiling with more spending cuts in an effort to satisfy the appetites of House Republicans.

Geithner said on NBC's "Meet the Press" that the White House will work parallel to the debt-ceiling debate to find other ways to cut spending, but "if we haven't worked all that out, we're still going to have to raise the debt limit."

On "This Week," Rep. Steve Southerland (R-Fla.) previewed the challenge the White House and House Speaker John BoehnerJohn Andrew Boehner4 reasons Mike Pompeo will succeed at Foggy Bottom The misunderstood reason Congress can’t get its job done GOP sees McCarthy moving up — if GOP loses the House MORE (R-Ohio) will face in persuading Tea Party lawmakers to sign on to raising the debt ceiling.

Southerland and other conservative Republican lawmakers warned that before they will sign on to raising the debt ceiling, they want to see spending caps and other dramatic steps taken to cut spending.

"We've got to have some guarantees," Southerland said.

Geithner was also asked Sunday if he will stay on for a second term with Obama.

The Treasury secretary demurred, but indicated he was enjoying the job.

"I've got a lot on my plate still. We've got a lot of challenges ahead," Geithner said. "I'm going to keep at trying to fix what's broken here."

— Erik Wasson contributed.

This story was updated at 11:45 a.m.