A bipartisan effort to rein in the national debt stalled Tuesday, as members of the Senate’s so-called Gang of Six signaled that an agreement is unlikely to come this week in time for the start of White House-led budget talks.

The absence of a deal deprives policymakers of a bipartisan centerpiece that could smooth the way toward agreement in the contentious battle between Democrats and Republicans over the appropriate size and shape of government.

Members of the Gang of Six said Tuesday that they are continuing to meet daily and that a deal is still possible. However, one of the six, Sen. Tom Coburn (R-Okla.), left town abruptly Tuesday because of a family emergency, leaving lawmakers and the White House as they begin negotiations over whether to allow the government’s debt to keep rising.

Treasury Secretary Timothy F. Geithner has said Congress must act by Aug. 2 to raise the legal limit on borrowing, currently set at $14.3 trillion, or risk the United States defaulting on its obligations. With the two parties far apart, work is proceeding on parallel tracks to forge an agreement on long-term deficit reduction, which many lawmakers on both sides say will be necessary to win their vote for a higher debt ceiling.

In addition to the Gang of Six talks, Vice President Biden is set to begin a series of meetings Thursday with Democratic and GOP representatives from both chambers. Republicans have indicated that in those talks they will try to advance the budget plan drafted by House Budget Chairman Paul Ryan (R-Wis.) and approved last month by House Republicans. That is increasing pressure on Senate Democrats to draft their own budget blueprint for fiscal 2012.

On Tuesday, Senate Budget Chairman Kent Conrad (D-N.D.) said time was running out for the Gang of Six to produce an agreement that he had hoped would form the basis for the Senate’s 2012 spending plan. Instead, Conrad — a member of the band of three Democrats and three Republicans who have been meeting for months behind closed doors — said he would proceed alone as soon as next week to come up with a blueprint that would incorporate many of the bipartisan group’s goals.

“I don’t know when or if they’ll reach a conclusion,” he said of the Gang of Six. “But I really can’t wait.”

Conrad said his framework would seek to trim deficits by $4 trillion over the next decade through sharp cuts in spending and an overhaul of the tax code aimed at generating revenue. He said his proposal would not include changes to Social Security, a key element of the Gang of Six talks, and would make only modest changes to other entitlement programs.

Conrad denied that his decision to move forward reflected a lack of confidence in the Gang of Six process, which is widely viewed as the most promising avenue for bipartisan progress on the hardest issues facing lawmakers, such as tax and entitlement reform.

“I am still very actively engaged in the Group of Six and very hopeful that we’ll produce a result,” he said, “but it may not be in time to be a part of the budget resolution.”

It was unclear Tuesday whether Conrad’s move was intended to pressure the Gang of Six, who after meeting at least three times this week were said to be hung up on a number of sensitive details. Among them: how to design mechanisms that would force congressional committees to meet an array of spending and tax targets over the next two years.

Conrad’s plan did not find quick favor in his own party, where many liberals are adamantly opposed to the Gang of Six approach, which they view as ceding too much ground to the Republican call for sharp cuts to the social safety net. After Conrad detailed his plan at a private luncheon of Senate Democrats and their independent allies, Sen. Bernard Sanders (I-Vt.), a Budget Committee member, raged that it would “balance the budget on the backs of the sick, the elderly and the poor, who are already hurting.”

Sen. Benjamin L. Cardin (D-Md.), also a member of the budget panel, said he would favor a plan based on the approach of “shared sacrifice” espoused by the Gang of Six and President Obama’s fiscal commission, but only if Republicans also signed on. Such a blueprint, Cardin said, would be acceptable “as a starting point” for Democrats.

Senate Majority Leader Harry M. Reid (Nev.) cautioned lawmakers to withhold judgment on the Conrad proposal — or any other — until the debate is more fully engaged.

“At this stage, they should all be very, very careful signing onto a piece of legislation until we know what the endgame is,” Reid told reporters. “There are a lot of things floating around here. . . . Let’s not be signing onto all this stuff until we really know where we’re headed.”

Republican leaders, meanwhile, seemed dismissive of Conrad’s budget and the Gang of Six efforts, with Senate Minority Leader Mitch McConnell (Ky.) turning attention toward the Biden talks. That effort, he said, “will, in my view, lead to some kind of conclusion.”

Sen. Jeff Sessions (Ala.), the senior Republican on the Senate Budget Committee, echoed that position, encouraging the parties to stage an open debate rather than leaving such consequential decisions to the Gang of Six.

“We do have some differences of view on deeply important issues, and I say let’s have it out,” Sessions told reporters. “The idea that there will just be harmony out of an agreement that would change the course of America probably is expecting too much.”