The Virginia Republican said in a statement that the Republican-dominated House simply won’t support tax increases, and that he wouldn’t participate in the budget meeting scheduled for Thursday. Cantor said that it’s time for President Barack Obama to weigh in directly on the budget because Democrats insist on negotiating some tax increases.

A spokesman for Jon Kyl of Arizona, who’s representing Senate Republicans in the talks, said Kyl would not attend Thursday’s scheduled meeting either.

The moves seem aimed at drawing Obama more directly into the talks. Cantor expressed frustration earlier this week that the president had not been more involved. Whether the tactic generates hard feelings that could jeopardize an agreement remains to be seen.

Cantor said that plenty of progress has been made in identifying trillions of dollars in potential spending cuts to accompany legislation to raise the $14.3 trillion cap on the government’s ability to borrow money. Passage of the legislation this summer is necessary to meet the government’s obligations to holders of U.S. Treasuries. The alternative is a market-shaking, first-ever default on U.S. obligations.

Senate Finance Committee Chairman Max Baucus, D-Mont., said that including tax increases on the wealthy is only fair, and that he’s disappointed that Cantor has left the talks.

Baucus said that almost every deficit reduction deal in the past has involved a mix of tax increases and spending cuts. He said upper income Americans have seen a significant increase in wealth, so balancing the budget only through cuts in programs that serve the middle class and the poor is not fair.

"Revenues must be included so everyone can participate in addressing a critical national problem," Baucus said.

Cantor said that once the tax issue is solved, negotiators could quickly seal agreement.

"It is time for the president to speak clearly and resolve this 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."

The Biden-led group has been meeting since early May, trying to come up with areas of agreement on curbing a budget deficit that’s requiring the government to borrow more than 40 cents of every dollar it spends. Areas of tentative agreement include trimming farm subsidies, auctioning electromagnetic spectrum to communications companies, and cutting student loan subsidies.

But with Republicans unwilling to accept some higher taxes — even in the wake of a sweeping Senate vote to eliminate the ethanol tax subsidy — Democrats were unwilling to agree to tougher steps like curbing Medicare and Medicaid.

All along, it was anticipated that the Biden group would only be able to get so far and that the toughest decisions, such as taxes and cuts to federal health care programs, would be kicked upstairs to Obama and House Speaker John Boehner, R-Ohio. That duo sealed agreement in April on legislation to fund the government through the end of September.

"I would to expect to hear from (Obama)," Boehner said Thursday. Of Cantor’s decision, Boehner said: "I understand why he did what he did. I think those talks could continue if they’re willing to take the tax hikes off the table."

There are only 5 ½ weeks remaining until an Aug. 2 deadline for enacting an increase in the nation’s debt limit to prevent a U.S. default. Economists warn that could damage the nation’s credit rating and force the government to pay higher interest rates to continue to borrow the $125 billion a month it needs to finance its operations.

But increasing the borrowing cap is a politically poisonous vote for lawmakers, especially the tea party-backed Republicans controlling the House. Even while there’s agreement between Obama and top congressional leaders that the debt cap simply has to be raised, a majority of the public — especially core conservative GOP supporters — says the debt limit shouldn’t be lifted.

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AP writer Ricardo Alonso-Zaldivar contributed to this story.