House Speaker John Boehner, clearly frustrated after a closed-door meeting with Treasury Secretary Timothy Geithner, said President Obama's money man offered no "specific" plan for averting the looming end-of-year fiscal crisis, adding: "This is not a game."
"First, despite the claims that the president supports a balanced approach, Democrats have yet to get serious about real spending cuts," the Ohio Republican said. "And secondly, no substantive progress has been made in the talks between the White House and the House over the last two weeks."
Obama dispatched Geithner and White House Legislative Director Rob Nabors to meet separately Thursday with Boehner, as well as with Senate Majority Leader Harry Reid, Senate Minority Leader Mitch McConnell and House Minority Leader Nancy Pelosi.
The sessions were seen as an important step in determining how the government will avoid a year-end package of tax increases and spending cuts that could throw the economy into recession.
Reid, meanwhile, said Democrats are still waiting for a reasonable proposal from Republicans on how to avoid a potential financial meltdown. And the White House on Thursday called Boehner's demand that any increase in debt limit be matched in cuts "irresponsible."
"Asking that a political price should be paid to ensure Congress does its job... is deeply irresponsible," White House press secretary Jay Carney told reporters.
Republican lawmakers and the White House are at odds, in particular, over Obama's push to let lower tax rates expire for wealthier Americans.
Obama's tax plan calls for an extension of the existing tax rates for most Americans, while allowing for tax rates to increase for the wealthiest 2 percent.
Carney on Thursday called the president's approach "very pragmatic," saying, "he believes that it is entirely appropriate, as the American people do, that the wealthiest should be asked to pay a little bit more as we develop a balanced package for long-term deficit reduction.
"And he believes that the right way to do it, because it is mathematically sound and it is the simplest way, is to extend tax cuts for 98 percent of the American people, but not extend tax cuts for the top 2 percent ... and also to write into law some of the other changes that he's proposed that include caps on deductions of 28 percent and include other loophole closures.
"But he's open to ideas," Carney added.
Obama has chosen to delegate discussions with lawmakers to his team until the makings of a deal firm up enough for him to engage directly. He met with the four leaders on Nov. 16 and spoke with Boehner and McConnell by phone last week.
The president also spoke again with Boehner on Wednesday, a source familiar with the conversation told Fox News. A senior administration official would not characterize what was said on the call or say if a face-to-face meeting is planned. Boehner described the conversation with Obama Wednesday as "direct and straightforward."
The White House and Congress are trying to reach a deal before Jan. 1 – when all of the Bush-era tax cuts are set to expire and huge reductions to the federal budget kick in automatically. Those spending cuts are part of a default agreement by Congress after it failed to reach a more measured deal to reduce the trillion-dollar annual deficits that have brought the national debt to more than $16 trillion.
The mix of tax increases and budget cuts will equal roughly $100 billion alone next year and about $1.2 trillion over the next 10 years should Congress and the White House fail to reach a deal. Some economists say that could plunge the economy into a recession.
On the Senate floor Thursday, McConnell said raising tax rates during tough economic times is the "last thing we want to do."
"We’re not insisting on keeping tax rates where they are to protect some sliver of the electorate," the Kentucky Republican told lawmakers. "We’re insisting on keeping tax rates where they are, first and foremost, to protect jobs. And because we don’t think government needs the money."
"A lot of people around here seem to have forgotten that we’re still in the middle of a jobs crisis. I can tell you a lot of folks are hurting in Kentucky. National unemployment’s still just a hair below 8 percent, and millions of Americans are still looking for work," he continued. "So if it’s an iron law of economics that you get less of what you tax, why on earth would we want to raise taxes on work?
"Rates matter because they affect behavior. The higher the tax rate, the higher the disincentive to work," he said.
At least one Republican lawmaker has already left party ranks to say the GOP should accept the president's tax proposal.
Conservative Oklahoma Rep. Tom Cole, for instance, told GOP colleagues in a private meeting Tuesday that it's better to make sure that tax cuts for the 98 percent of taxpayers who make less than $200,000 or $250,000 a year are extended than to battle it out with Obama and risk increasing taxes on everyone.
Cole's remarks are noteworthy because he's a longtime GOP loyalist and a confidant of House Speaker John Boehner, R-Ohio. They were made in a meeting of the House GOP Republican whip team, which is a sounding board for GOP leaders.
"If we don't believe taxes should go up on anybody, why can't we accept a deal that takes 98 percent out and still leaves us free to fight on the other grounds," Cole said in an interview on Wednesday. "I'm not for using the American people for leverage or as a hostage.”
Fox News' Kelly Chernenkoff, Peter Doocy, Chad Pergram and The Associated Press contributed to this report.