Tea party champion Sen. Jim DeMint accused Treasury Secretary Timothy Geithner on Sunday of being like “Chicken Little” and exaggerating the consequences of failing to raise the nation’s borrowing capacity by Aug. 2, even as top Republicans have acknowledged the seriousness of the deadline.

The South Carolina Republican urged his colleagues not to rush to any deal currently being negotiated with Democrats because government default is not imminent.

“There certainly would be disruption, but this is not a deadline that we should rush and make a bad deal,” DeMint said on “Fox News Sunday.” “Secretary Geithner has been irresponsible. He’s playing Chicken Little here. The fact is that we will pay our debts if it’s the last dollar we have. … We’re not going to default.”

Geithner dismissed debt limit doubters on Sunday as irresponsible participants in “political theater.”

“There’s no responsible leader that argues that is a credible path. … It’s a political moment. People are trying to get attention,” he said on CBS’ “Face the Nation.” “They say really amazing things, but there’s no credible argument; no responsible leader would say for the first time in its history [the United States] should not pay its bills and meet its obligations. That would be catastrophic for the economy, and everybody understands that.”

The rhetoric from DeMint and his counterparts in the House Republican Study Committee demonstrate the difficulty faced by Republican leaders in trying to rally their caucuses around any deal in the coming weeks.

The fundamental disbelief in the seriousness of the August deadline, paired with the tea party opposition to government spending and a new insistence on passing a balanced budget amendment to the Constitution that could never clear the Senate, complicates the math for Speaker John Boehner (R-Ohio) and, to a lesser extent, Senate Minority Leader Mitch McConnell (R-Ky.).

Boehner, who has been engaged with the White House in trying to get a deal soon, has said that the August deadline is critical.

“While some think we can go past Aug. 2, I frankly think it puts us in an awful lot of jeopardy and puts our economy in jeopardy,” he said Friday.

McConnell, who appeared before DeMint on “Fox News Sunday,” was asked what would happen if a deal were not struck. He paused before essentially saying he would cross that bridge when he gets there.

“Well, we’re going to go forward, and I’ll have more to say about that later in the week,” McConnell said. “There’s always a contingency plan.”

Administration officials have been quietly working to shore up an alternative plan if Congress fails to approve an extension of the nation’s borrowing capacity by early August. Geithner already has moved the deadline twice by rearranging funds in places like federal pension programs, but he says that the moves he would need to make next would be more drastic and likely affect the financial markets.

DeMint, however, stood firm on his call for a balanced budget amendment. House conservatives are standing strong on the constitutional change, and even though all 47 Senate Republicans support it, veteran lawmakers such as Sen. John McCain (R-Ariz.) have openly criticized colleagues for intending to hold the debt limit hostage to a policy goal that is unlikely to be met this Congress.

“We will give the president an increase in the debt limit in return for some reasonable cuts in spending this year, some caps in spending over the next 10 years and his agreement to send a balanced budget amendment to the Constitution to the states for them to ratify,” DeMint said.