House Speaker John Boehner expressed doubt Tuesday about President Obama’s warning that if the nation’s $14.3 trillion debt limit is not raised by Aug. 2, the elderly may not get their Social Security payments.

“I don’t know what to believe,” Boehner told Fox News’ Bret Baier in exclusive interview after the latest White House meeting with congressional leaders.

“The Treasury secretary is going to have options in terms of who should be paid and who shouldn't,” he said. “Yes, there are some debts that have to be rolled over. But there’s going to be money available on Aug. 3, and I think it’s way too early to be making some types of veiled threats like that.”

Obama told CBS News earlier Tuesday that the political stalemate over increasing the nation’s legal borrowing limit could jeopardize Social Security payments.

“I cannot guarantee that those checks go out on Aug. 3 if we haven’t resolved this issue,” he said. “Because there may simply not be the money in the coffers to do it.”

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The dispute over the impact of not raising the debt limit is just the latest disagreement between two sides who have not been able to find much to agree on in White House negotiations to avert what would be the first-ever government default.

Republicans refuse to consider any tax increases, while Democrats are insisting on new revenues to go along with deep spending cuts.

Senate Minority Leader Mitch McConnell, R-Ky., said the president has only given Republicans three options: smoke and mirrors, tax hikes or default. And he claimed Republicans choose none of the above.

“After years of discussions and months of negotiations, I have little question that as long as this president is in the Oval Office, a real solution is probably unattainable," he said.

Senate Democrats say they don’t support fixing entitlements unless it is part of a grand debt plan.

“I will not touch Medicare for some simple, little deal that we get nothing that’s beneficial to the country,” Senate Majority Leader Harry Reid said.

Earlier Tuesday, Boehner told House Republicans behind closed doors that when it became clear the White House would only agree to entitlement reform if it came along with tax hikes, he walked away.

“Am I angry about it? I sure as hell am,” he said. “I believe we are missing a great opportunity.”

In public, the speaker turned his anger toward the president.

“This debt limit increase is his problem,” Boehner said. “The president talks a good game but when it comes time to actually putting these issues on the table, making decisions, he can’t quite pull the trigger.”

Despite the tougher talk, aides say behind closed doors the tone in the White House meetings has been frank and constructive and Treasury Secretary Timothy Geithner reiterated Congress realizes something must get done.

“Default is not an option. Failure is not an option,” he said.

Ahead of Tuesday’s third meeting, McConnell unveiled his last choice plan to make sure default is not an option: Congress would authorize $2.5 trillion in three installments with serious strings attached.

“I would advocate that we would pass legislation giving the president the authority to request of us an increase in the debt ceiling that would take us past the end of his term,” he said.

Boehner told Fox News that McConnell's proposal makes for a good backup plan.

"I think everybody believes there needs to be a backup plan," he said.

Fox News' Mike Emanuel contributed to this report.