Updated: 6:54 p.m.

After Republican deputies abandoned debt talks Thursday, the negotiations are now squarely in the hands of the top leaders — Speaker John Boehner, President Barack Obama and Senate Majority Leader Harry Reid — whether or not they’re ready to tackle the massive task.

House Majority Leader Eric Cantor (R-Va.) and Senate Minority Whip Jon Kyl (R-Ariz.) decided to walk out of talks led by Vice President Joseph Biden after declaring an impasse over Democrats’ demands for a tax increase to accompany trillions of dollars in spending cuts. But Reid said Thursday he had not yet been contacted to join in any new high-level negotiations.

According to White House press secretary Jay Carney, Obama and Boehner met Wednesday night at the White House. Carney would say only that the meeting was designed “to discuss a variety of issues, following up on conversations he had with him on the golf course.”

Carney also confirmed that Cantor had called Biden on Thursday to inform him he would no longer attend the meetings. A GOP aide also said Cantor informed other GOP leaders including Boehner, Kyl and Jeb Hensarling (Texas) before he announced his decision.

Despite private grumbling among some Republicans that Cantor had essentially blown up the talks while the GOP was still holding the ball, Carney said the end of the Biden-led negotiations simply marks a new phase of the effort to tackle the debt limit.

“It has always been the case where these talks would proceed to a point where the remaining areas of disagreement would be addressed by leaders and the president,” Carney said.

“This process is sort of proceeding as envisioned,” he added.

A GOP aide agreed, arguing Cantor’s decision was aimed at “changing the dynamic” of the negotiations after they had entered their most difficult phase.

Biden cited “significant progress” by the negotiators over the past several weeks and said the process was transitioning as planned.

“As all of us at the table said at the outset, the goal of these talks was to report our findings back to our respective leaders,” he said in a statement late Thursday afternoon. “The next phase is in the hands of those leaders, who need to determine the scope of an agreement that can tackle the problem and attract bipartisan support. For now the talks are in abeyance as we await that guidance. We stand ready to meet again as necessary.”

But Reid said Thursday that he’s “terribly disappointed” that Republicans have abandoned deficit talks with Vice President Joseph Biden, and the Nevada Democrat pledged to keep working to find a solution.

“It appears they are giving up,” Reid said. “We can’t give up. The issues are far too serious.”

Reid said he hopes the Republicans reconsider. “We have to act like adults here,” he said.

Asked if he would join direct talks with Boehner and Obama, Reid said “I haven’t been invited to a meeting yet.”

Still, Reid said the issue now appears to be in the hands of the top leaders, and he dismissed the idea raised by some Senators that this could give an opening for a revival of the bipartisan “gang of six” to fill the vacuum.

“My honest feeling is that I think we’re beyond gangs of five and gangs of sixes,” he said. The gang of six — Sens. Dick Durbin (D-Ill.), Mark Warner (D-Va.), Kent Conrad (D-N.D.), Saxby Chambliss (R-Ga.), Michael Crapo (R-Idaho), and Tom Coburn (R-Okla.) — essentially collapsed when Coburn last month pulled out of those talks.

Senate Finance Chairman Max Baucus (D-Mont.), one of the two negotiators for Senate Democrats in the Biden talks, also said he was disappointed at Kyl and Cantor’s decision. “Our deficit problem is too important to walk away,” he said, reiterating that a balanced approach is needed.

“There has to be some revenue,” he said. “I’m hopeful this is merely a temporary setback.”

Sen. Charles Schumer (D-N.Y.), the No. 3 Democratic leader, said Cantor seemed to be “spooked” by the need for a compromise in the talks and walked out. “This was not an adult moment,” the party’s messaging chief said.

Schumer said a final deal cannot cut Medicare benefits and must generate revenue by eliminating wasteful subsidies and loopholes and do something to generate jobs in the short term, including tax cuts. Likewise, Carney indicated the president would not sign onto a deal that cut Medicare but continued to allow “millionaires and billionaires” to receive tax cuts.

Rep. Chris Van Hollen (Md.), who was part of the House Democrats’ representation in the Biden talks, told reporters Thursday he is “disappointed that Leader Cantor has chosen to leave the talks. They had been proceeding well, although there was no doubt that there were some very difficult issues that needed to be decided.”

He added: “The Speaker of the House said it was time for an adult moment. An adult moments means it’s time for making tough decisions. And the reality is: Until our Republican colleagues are more concerned about the need to reduce the deficit than they’re worried about what Grover Norquist will say, we’re going to have a really difficult time reducing the deficit.”

Minority Leader Nancy Pelosi said she did not hear about Cantor’s news until after she left a deficit reduction meeting at the White House on Thursday morning. And until Thursday, the California Democrat said, she had thought the bipartisan talks were constructive and moving ahead.

“We left the meeting to find that Leader Cantor had walked out of meetings,” Pelosi said. “He said he has walked out of the meetings because Democrats want to raise taxes. Yes, we do want to remove tax subsidies for Big Oil. We want to remove tax breaks for corporations that send jobs overseas. That list goes on. I don’t know that that’s a reason to walk away from the table when we are trying to find a balanced approach.”

Jessica Brady contributed to this report.