ASHINGTON (AP) — The top two Republicans in Congress sought Tuesday to put the onus on President Barack Obama for failure to resolve a fight over how to increase the government's borrowing authority. Senate Minority Leader Mitch McConnell said a deal with Obama is "probably unattainable" and House Speaker John Boehner said the specter of default is "his problem."

The unusually blunt and combative language came just hours ahead of another White House meeting aimed at finding an accommodation on a package of spending cuts to accompany an increase the debt limit. It further complicated an already convulsive bargaining environment, with the Aug. 2 debt limit extension deadline fast approaching.

McConnell maintained that White House offers to cut long-term spending amount to "smoke and mirrors" and directly challenged Obama's leadership. After years of discussions and months of negotiations," the Kentucky Republican said, "I have little question that as long as this president is in the Oval Office, a real solution is probably unattainable."

Said Boehner: "This debt limit increase is his problem and I think it's time for him to lead by putting his plan on the table — something that Congress can pass. Where is the president's plan? When's he going to lay his cards on the table?"

McConnell charged in a Senate floor speech that Democrats and the Obama administration were relying on budget gimmicks to give the "appearance of serious belt-tightening."

White House spokesman Jay Carney said the Republican reaction Tuesday "was unfortunate."

"Sometimes there's rhetoric put out there in public that doesn't match what has often been very constructive and respectful conversations in meetings," Carney told reporters. He added: "By fits and starts, the process continues to move forward."

Responding to Boehner's comment, Carney pointed out that it is Congress' responsibility to vote for an increase in the debt ceiling.

"The president doesn't have a vote in this," he said. "It's Congress that has to act." He said Obama will be in office for at least another 18 months, and "the American people expect Congress to work with him."

Obama has been pushing for $4 trillion in a 10-year deficit reduction proposal in hopes of freeing votes to increase the government's borrowing authority. But Boehner, after seeking to forge a deal of that magnitude, told the president that a smaller, $2 trillion to $2.4 trillion deal was more realistic. A deal is essential to win Republican votes to increase the nation's debt ceiling by Aug. 2, or risk a government default.

McConnell said Republicans will "do the responsible thing and ensure the government doesn't default on its obligations."

But he dismissed the cuts the administration and Democrats have proposed. Republicans say Democrats want most of the spending cuts to be concentrated in the later years of a deal. They say that despite promising cuts of $1.1 trillion from Cabinet agency operating budgets, the White House is insisting on a two-year freeze in such spending at the current level of $1.05 trillion.

McConnell's and Boehner's heightened criticisms come as Obama has increasingly used public appearances, including a news conference Monday and a network television interview Tuesday, to take his case to the public. Obama has argued that both Democrats and Republicans need to make politically painful decisions and has portrayed Republicans as intransigent.

As the debate intensified, both sides looked for signs, subtle or otherwise, that negotiations were souring.

In an interview with CBS Tuesday, Obama seemed to back off his unequivocal assurances that the debt ceiling would be raised, thus avoiding a first-ever default.

CBS anchor Scott Pelley asked Obama if he could guarantee that Social Security checks would go out on Aug. 3, the day after the administration says the government would go into default.

"I cannot guarantee that those checks go out on August 3rd, if we haven't resolved this issue.," Obama replied in an excerpt of the interview released by CBS. "Because there may simply not be the money in the coffers to do it."

Earlier, Treasury Secretary Timothy Geithner stressed that no one in government would let a government default occur.

"Let me be clear: the debt limit will be raised," Geithner told a Women in Finance Symposium Tuesday. "Failure is not an option. Both sides understand what is at stake and will come to an agreement."

He said Obama is willing to make spending cuts across the government "as long as they are done responsibly, over time."

Until today, Republicans had so far focused their criticism on Obama's demand for new tax revenues in the final deficit reduction package. But McConnell's tone indicated a new line of attack based on competing versions of how much progress had been made in talks led by Vice President Joe Biden in May and June.

McConnell accused the administration of leaking its proposals for spending cuts to the media without details.

"The lack of detail concealed the fact that the savings they were supposedly willing to support were at best smoke and mirrors," the Kentucky Republican said.

On Monday, House Majority Leader Eric Cantor, R-Va., a participant who left the Biden talks last month because of Democratic demands on taxes, spelled out potential spending cuts that had been identified. But Democratic lawmakers made clear that such a cutting-only approach without tax increases on wealthier Americans would never pass the Democratic-led Senate or the House, where Democratic votes would be needed, too.

Cantor, aides said, outlined up to $2.3 trillion in spending cuts over the upcoming decade, with $1.3 trillion coming from squeezing the day-to-day budgets of Cabinet agencies, including the Pentagon.

Cantor erred on the high end of the savings range in virtually every instance. The White House countered that the cuts really approached $1.7 trillion or so, which would leave negotiators $700 billion short of the $2.4 trillion being sought.

Democratic officials familiar with Obama's private talks with leaders of the House and Senate insist that Congress will not let the government go into default for the first time in American history — and that Republicans, ultimately, would vote to raise the debt limit even if a deficit-cutting package does not come together over the next two weeks.

Republicans say they won't allow a default, but that a major reduction in spending must come as part of the package — and therefore both sides remain in a stalemate on the debt limit.

After Monday's White House meeting, neither side showed any give that might generate hopes for a speedy agreement. Instead, Republicans again took a firm stand against revenue increases while Obama and his Democratic allies insisted that they be part of any equation that cuts programs like Medicare.

"I do not see a path to a deal if they don't budge, period," Obama said on Monday.

At the same time, the president turned up the pressure by announcing he won't sign any short-term debt limit increases.

"We are going to get this done," Obama insisted during a news conference.

Obama's declaration seemed aimed at pressuring lawmakers to continue to strive for the largest deficit reduction plan possible, even though hopes for a "grand bargain" mixing a complete overhaul of the tax code with cuts to benefits programs like Medicare and Social Security fizzled over the weekend.

The Treasury Department says lawmakers have until Aug. 2 to extend the nation's debt limit to prevent a catastrophic government default on its bills. With that deadline fast approaching, the public is growing more concerned about what happens if Congress and the White House can't reach a deal.

Forty-two percent of Americans say they see a greater risk to the economy from not raising the debt limit, according to a Washington Post-Pew Research Center poll conducted last week. That's up 7 points from late May. However, there are still 47 percent of Americans who say they are more concerned about the consequences of raising the debt ceiling.

The business community is also upping the pressure on lawmakers, warning that a failure to increase the nation's borrowing limit could have an immediate impact on the economy recovery.

"An unprecedented default on the nation's bills would have dire consequences for our economy, our markets, and Main Street Americans," said Thomas Donohue, president of the U.S. Chamber of Commerce.

Despite lingering hopes for a larger deal, the goal of the White House talks is to produce spending cuts of at least $2.4 trillion or so over the coming decade. Such cuts wouldn't do enough to address deficits that threaten the economy, but they would represent a down payment on further reductions that would be imposed after next year's elections.

The $2.4 trillion figure would meet the House Republicans' own standard of a debt-cutting package: one that would exceed the size of the increase in the debt limit, and provide enough borrowing room to get the country through 2012.

Obama spent most of his time encouraging lawmakers to reconsider a bigger deal, on the order of some $4 trillion in spending cuts and tax hikes over 10 years. Democrats familiar with the talks said it was clear after the meeting that negotiators are going to have come up with some new ideas in hopes of finding a compromise.

As a measure of the political peril Obama is courting, the president is willing to discuss raising the Medicare eligibility age from 65 to 67 years, provided Republicans would allow Bush-era tax cuts for the wealthy to expire at the end of 2012 and agree to other unspecified demands, according to a Democratic congressional aide.

All the officials familiar with the talks spoke on condition of anonymity to disclose details of the private discussions.