Updated: 1:05 p.m.

House Majority Leader Eric Cantor (R-Va.) and Senate Minority Whip Jon Kyl (R-Ariz.) pulled out of bipartisan debt talks led by Vice President Joseph Biden after declaring an impasse over taxes and insisting the president himself get involved in the discussions.

Cantor said Thursday that the group had identified trillions in spending cuts but that the votes simply aren’t there in the House to include tax increases and revenue-raisers that Democrats are demanding. Instead, he put the onus of finding a deal on Speaker John Boehner (R-Ohio) and President Barack Obama.

“Given this impasse, I will not be participating in today’s meeting and I believe it is time for the president to speak clearly and resolve the tax issue,” Cantor said. “Once resolved, we have a blueprint to move forward to trillions of spending cuts and binding mechanisms to change the way things are done around here.”

In a joint statement, Kyl and Senate Minority Leader Mitch McConnell (R-Ky.) said, “A bill with new spending and higher taxes would fail with bipartisan opposition — as it should. President Obama needs to decide between his goal of higher taxes, or a bipartisan plan to address our deficit. He can’t have both. But we need to hear from him.”

Also on Thursday morning, McConnell called the Democratic demand for taxes “mystifying” given the state of the economy and the fact that both Republicans and Democrats have voted against raising taxes several times in the past year.

“We’ve known from the beginning that tax hikes would be a poison pill to any debt reduction proposal,” the Kentucky Republican said. “Those who are proposing them now either know this or they need to realize it quickly.”

McConnell also ripped Senate Democrats for calling for more stimulus spending as part of the deal.

“What planet are they on?” he asked.

Boehner in a Thursday press conference said he backed Cantor’s statement that taxes can’t be part of a deal, but he declined to say whether he had endorsed Cantor’s decision.

“I understand why he did what he did,” Boehner said.

He added, “Since the beginning, the Majority Leader and myself, along with Sen. McConnell and Sen. Kyl, have been clear — tax hikes are off the table.”

The decision by Cantor had some Democrats speculating about his intramural rivalry with Boehner. Although Cantor won’t be able to take credit for getting a deal, he got Democrats to show some leg on trillions of dollars in spending cuts without having to give up the GOP crown jewel of opposing tax increases.

Now, if there is a final deal that upsets the GOP base, it will be on Boehner, not Cantor.

“Eric Cantor just threw Boehner under the bus,” one Democratic aide said. “This move is an admission that there will be a need for revenues, and Cantor doesn’t want to be the one to make that deal.”

Democrats also criticized Cantor for pulling out.

“When the going gets tough, Cantor gets going,” another Senate Democratic aide said. “Republicans haven’t been getting their way on cutting Medicare, plus since the ethanol vote, there’s been a growing consensus among even Republicans that revenues need to be part of the final solution. This was clearly too hot for Cantor to handle, and now he wants to kick the final deal-making upstairs to the Speaker’s office.”

From the beginning, there had been skepticism that the Biden group could reach a compromise given the partisans on each side, with an expectation that Obama, Boehner and Senate Majority Leader Harry Reid (D-Nev.) would have to cut a deal just as they did earlier this year on a continuing resolution to avoid a government shutdown.

And it also dashes hopes for now from Democrats that a Senate vote to eliminate ethanol subsidies might lead Republicans to agree to close other tax breaks and loopholes to reduce the deficit.

Still, lawmakers have an imperative to get something done before the government hits a potentially catastrophic default on its more than $14 trillion in debt. Treasury Secretary Timothy Geithner has warned that could happen as soon as Aug. 2.

Joseph Schatz, Emily Pierce and Jessica Brady contributed to this report.