Updated, 12:30 p.m.

House Majority Leader Eric Cantor (R-Va.) on Thursday announced that he was pulling out of the debt-limit talks being led by Vice President Biden, citing an impasse over whether tax increases should be included in any comprehensive deficit-reduction plan.

“There is not support in the House for a tax increase, and I don’t believe now is the time to raise taxes in light of our current economic situation,” Cantor said in a statement. “Regardless of the progress that has been made, the tax issue must be resolved before discussions can continue.”

In an interview, Senate Majority Leader Harry M. Reid (D-Nev.) expressed disappointment that Cantor would drop out “when we’re at such a crucial time.”

“I guess he wanted to meet directly with the president. Biden was briefing the president every day. ... So I don’t understand why he decided he didn’t want to be part of this. Maybe that was part of the original plan--that he’d go so long and then turn it over to Boehner,” Reid said.

Reid added that he feared that “the Republicans are playing a game of chicken” against the Aug. 2 deadline. “If they don’t work to cooperate to get something done, the harm for this country and the world will be very significant. And that’s on their conscience,” Reid said.

News of Cantor’s exit from the talks, first reported Thursday morning by the Wall Street Journal, came hours before the seven-member working group was to hold its eleventh meeting since it was first formed in May.

“We’ve reached the point where the dynamic needs to change,” Cantor said in an interview with the Journal. “It is up to the president to come in and talk to the speaker. We’ve reached the end of this phase. Now is the time for these talks to go into abeyance.”

In the statement released Thursday morning, Cantor said Biden “deserves a great deal of credit for his leadership in bringing us this far” and said that the group had “identified trillions in spending cuts, and to date, we have established a blueprint that could institute the fiscal reforms needed to start getting our fiscal house in order.”

“That said, each side came into these talks with certain orders, and as it stands the Democrats continue to insist that any deal must include tax increases,” Cantor said. “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 added that once the tax-increase issue is 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.”

Later Thursday, Senate Republican Whip Jon Kyl (R-Ariz.) and Senate Republican Leader Mitch McConnell (R-Ky.) released a statement supporting Obama’s direct involvement.

“A bill with new spending and higher taxes would fail with bipartisan opposition – as it should,” they said. “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.”

Rep. Xavier Becerra (D-Calif.), the vice-chairman of the House Democratic Caucus, in a statement Thursday criticized Cantor’s move.

“Instead of making the hard choices to find a responsible way to reduce the deficit, Republicans are running away from the mess they created,” said Becerra, who is not involved in the debt-limit talks but was previously a member of Obama’s bipartisan fiscal commission. “Is this the adult moment they promised the American people in November?”

In the Biden group’s previous meetings, members had expressed cautious optimism that they were on track to reach their goal of devising a comprehensive deficit-reduction framework by July 1, with President Obama, House Speaker John Boehner (R-Ohio) and Senate Majority Leader Harry Reid (D-Nev.) likely to hash out the final details of a plan before the Treasury Department’s Aug. 2 deadline for Congress to vote on raising the country’s debt limit.

But Biden cautioned after last week’s meetings that this would be the week the group would attempt to tackle the big philosophical differences between the parties – on tax increases, health care spending and entitlement reform. Democrats and Republicans remain far apart on those issues, and it appeared to be a tall task for the Biden group to overcome those differences on such a tight deadline.

Staff writers Paul Kane and Rosalind S. Helderman also contributed to this story.