Senator Harry Reid, the Nevada Democrat and Senate majority leader, also said he expected that the talks would resume at a higher level, though he provided no timetable.

“With what Kyl and Cantor’s done, I think it’s in the hands of the speaker and the president and, sadly, probably me,” he told reporters.

While it had been assumed that the Congressional leaders and Mr. Obama would ultimately have to strike the final deal, the Biden talks were expected to extend at least through the end of the month. The Republican withdrawal was an unexpected and sudden interruption.

Congressional Democrats expressed disappointment at Mr. Cantor’s decision and maintained that revenues must be part of any agreement.

“We cannot balance the budget solely on the backs of the middle class,” said Representative James E. Clyburn, Democrat of South Carolina, a member of the House leadership taking part in the talks. “We simply must forge a bipartisan agreement. Failure is not an option, and I hope a bipartisan resolution will be achieved.”

Democrats have repeatedly said that they could not support a budget deal that relies solely on spending cuts and other program changes to produce the more than $2 trillion in savings. Officials said Wednesday’s negotiating session was unusually tense as Democrats sought to get Republicans to commit to some revenue increases in exchange for Democratic concessions on spending cuts.

Republicans knowledgeable about the events said Mr. Cantor decided to withdraw from the discussions because of the continuing emphasis by Democrats on potential new revenues. They said that he, Speaker John A. Boehner, Mr. McConnell and Mr. Kyl had previously discussed their discontent with the Democratic push for revenues and that some action was necessary to change the dynamic of the talks and show that Republicans were serious about not accepting what amounted to a tax increase.