"No substantive progress has been made in the talks between the White House and the House over the last two weeks," Boehner said.
Differences between the parties include the scope of a deficit deal, with Republicans insisting that Social Security reforms be part of it while Democrats say the government pension system is self-funded and therefore plays no role in federal deficits.
Obama also wants any deal reached in the current session of Congress to include an increase in the federal debt ceiling, which is expected to be needed as soon as February or March.
To Boehner and Republicans, the debt ceiling is a valuable negotiating tool to extract concessions from the Democrats and the president.
"Any increase in the debt limit has to be accomplished by spending reductions that meet or exceed it," Boehner declared Thursday, saying Obama would have to pay a price to raise the ceiling on federal borrowing.
Carney responded to Boehner's demand of a price by calling such brinksmanship over the credit standing of the nation "entirely inappropriate."
"Asking that a political price be paid in order for Congress to do its job to ensure that the United States of America pays its bill and does not default for the first time in history is deeply irresponsible," Carney said.
A similar battle over the debt ceiling, with threats of a government default on its obligations, led to the unprecedented downgrade of the U.S. credit rating last year by one agency.
Geithner is the Obama administration's point man in the talks. His separate meetings on Thursday with Boehner, House Democratic leader Nancy Pelosi, Reid and Senate Republican leader Mitch McConnell also included Rob Nabors, Obama's legislative affairs director.
Fresh off his re-election victory on November 6, Obama launched a campaign-style approach this week aimed at pressuring Republicans to pass his tax proposal.
In remarks Wednesday at the White House, Obama urged Americans to call, e-mail and tweet their members of Congress to urge immediate passage of his proposal to extend tax cuts for most Americans while allowing rates on the wealthiest 2% to increase to 1990s levels.
Obama's phone conservation with Boehner later Wednesday lasted 28 minutes, Carney said. A source familiar with the call said the president insisted any deal must include tax rates going up on the wealthiest Americans, a point Carney repeatedly emphasized to reporters Thursday.
Meanwhile, a rift among House Republicans on whether to give Obama what he wants became public Wednesday, with two conservatives saying the tax proposal would likely pass if brought to a vote.
Boehner immediately shot down the call by veteran Rep. Tom Cole of Oklahoma for the chamber to approve the Senate measure, saying he disagrees with his colleague. House GOP aides insisted there is no plan to bring the proposal up for a vote.
However, the public stance by Cole -- which echoed similar statements from conservatives in recent weeks -- as well as his prediction that the Senate proposal would pass in the House showed an increasing desire among House Republicans to move beyond an issue that has harmed them.
Conservative Rep. Tim Scott of South Carolina also said he thinks the Obama tax plan would pass the House, though he made clear to CNN he would oppose it.
Obama made clear Wednesday that he hopes public pressure will cause House Republicans to move from their unyielding stance.
"The lesson is that when enough people get involved, we have a pretty good track record of making Congress work," he said.
Cole and some other conservatives say such pressure is the reason to simply give the president what he wants and move past the immediate tax issue.
"If we agree that taxes shouldn't go up on 98% of the people, shouldn't we take that now and get that set aside and make sure they know their taxes aren't going up?" Cole said Wednesday night on CNN's "Anderson Cooper 360."
Sounding a lot like Obama, Cole said that "if we can give assurance to most Americans that their taxes are going to be fine, I think that's helpful to them in planning their lives going forward."
Obama argued Wednesday that settling the tax question for middle-class families would clear the way for the broader agreement everyone wants.
"We can do it in a balanced a fair way, but our first job is to make sure that taxes on middle-class families don't go up," Obama said. "And since we all theoretically agree on that, we should get that done. If we get that done, a lot of the other stuff is going to be a lot easier."
Boehner outlined a similar process on Thursday, but demanded more commitment from Obama and Democrats on spending cuts and entitlement reforms.
His framework includes what he called a "down payment" for the rest of this year that would include spending cuts and additional tax revenue, but not higher tax rates. That would set up negotiations on tax reform and other aspects of deficit reduction next year, Boehner said.