A bipartisan group of lawmakers from both houses urged the deficit-reduction supercommittee Wednesday to “go big” as it nears a deadline to avoid mandatory across-the-board cuts, telling the panel it has significant congressional support for a deal that would cut the deficit by about $4 trillion.

But Democrats and Republicans on the supercommittee later held separate meetings amid mounting pessimism that the 12-member panel would be able to reach an agreement.

“We need to find out about whether our Republican colleagues want to continue to negotiate or whether they’ve drawn a hard line in the sand,” said Rep. Chris Van Hollen (D-Md.), a supercommittee member.

The top Republican on the supercommittee, Rep. Jeb Hensarling (Tex.), backed away from his warning that GOP members have “gone as far as we feel we can go” on new tax revenue, telling reporters he would consider any offer by the panel’s Democrats. But he insisted that until the Democrats produce a counterproposal, the Republicans are “not changing” their own plan.

Earlier, in a Capitol Hill news conference, Republican and Democratic members of the House and Senate stressed that a “bold” plan is needed to convince markets and the international community that the U.S. government is capable of dealing with its debt issues.

Members of what has been dubbed the “go-big coalition” said about 150 lawmakers in both houses support a compromise deficit-reduction plan that would include increases in revenue and cuts to entitlement programs. About 40 members of the group attended the news conference.

“We want [the supercommittee] to know that there is a large and significant number of us in both chambers who want such a deal and are ready to give it a fair shot,” said Rep. Steny H. Hoyer (D-Md.), the House minority whip. “None of us want to risk the immediate and long-term effects of sequestration . . . if the committee fails.” He referred to the procedure, codified in this summer’s deal to raise the debt ceiling, that would trigger automatic across-the-board cuts of $1.2 trillion over 10 years. Under the sequestration requirement, annual cuts of $109.3 billion would start in fiscal 2013, with half the amount to come from the Defense Department — reductions that the Pentagon has warned could affect national security.

The coalition wants the supercommittee to know that “the right thing to do is to go big,” said Sen. Saxby Chambliss (R-Ga.). He said that could mean deficit reduction of $3 trillion to $6 trillion, instead of the minimum requirement of $1.2 trillion that the panel must agree on by a Nov. 23 deadline.

“I’m very proud to stand here with these folks today and say, ‘supercommittee, we got your back,’ ” Chambliss said.

Although several members of the coalition repeated that expression of support, they offered no specifics on how to reach a deficit-reduction deal in the range of $4 trillion, providing little more than encouragement from the sidelines as the supercommittee struggles to agree on how to achieve even the $1.2 trillion minimum.

Sen. Richard J. Durbin (Ill.), the second-ranking Democrat in the Senate, argued nevertheless that “going bigger is easier politically,” reasoning that reluctant members of Congress would find it more acceptable to support a truly “historic” package.

He urged Democrats and Republicans to view massive debt reduction as “the challenge of our political generation,” exhorting them: “This is our moment. Let’s seize that moment.”

But there were signs that the moment was slipping away, as Democrats on the supercommittee met on the first floor of the Capitol, while Republican panel members gathered nearby in the Cannon House Office Building. Republicans scattered afterward without speaking to reporters, while Democrats hinted darkly that the negotiations may be falling apart.

The panel’s Democratic chairman, Sen. Patty Murray (D-Wash.), said Democrats “are not going to accept a plan that gives a tax break to the wealthiest Americans and balances all of this incredible challenge we have on the backs of middle class families.” Murray said various members of the panel are continuing to talk, but it was not clear how the process would move forward.

Hensarling said Tuesday night that his side’s offer earlier this month — which included $250 billion in new revenues achieved through tax reform plus $50 billion through changing the measure of inflation used to calculate tax brackets — represented the most that GOP lawmakers were willing to concede on the issue of taxes.

But he told a hastily arranged news conference Wednesday afternoon that he was “willing to look at any offer” and urged Democrats to put forward a proposal “that actually reforms our entitlement spending and solves the problem.”

Until then, the chairman of the House Republican Conference added, the GOP supercommittee members are sticking with the proposal put forward on their behalf by Sen. Patrick J. Toomey (R-Pa.).

“That’s the offer,” Hensarling said. “We’re not changing this offer that we have on the table. I’m not going to negotiate with myself. But again, I’m still awaiting Democrats to put fundamental reform of our entitlements on the table.”

The developments came as White House officials quietly braced for the panel’s failure, with advisers privately expressing pessimism that it would find a way to reduce the deficit by $1.2 trillion. In public, however, Obama administration officials insisted that failure is not an option.

“I don’t think it makes sense to anticipate their failure,” White House Office of Management and Budget Director Jack Lew said Tuesday. “I think it’s important that they succeed. The president made that clear in the calls he made on Friday.”

Several members of the bipartisan coalition made similar points Wednesday.

“Failure can’t be an option,” said Sen. Mark R. Warner (D-Va.). “The whole rest of the world is watching.” He said the United States must avoid the kind of debt crisis that has afflicted European countries.

“Whether we like it or not, this debt and deficit debate has become, in effect, the proxy for whether our democratic institutions are up to to the job in the 21st century,” Warner said.

President Obama called the Democratic and Republican leaders of the supercommittee from Air Force One on his way out of town last week for an extended trip to Hawaii and Asia, and he has continued to urge action in his remarks on the road.

Obama has stopped short of issuing a blanket veto threat if the committee tries to undo the severe cuts that would take effect in 2013 if an agreement is not reached. Obama has simply said that Congress “must not shirk its responsibilities,” and, in a news conference from Hawaii, he said he would not comment on the potential for a veto.

If lawmakers on the committee fail to reach agreement by next week’s deadline, Obama may be forced to step back into the fray after taking a steadfastly hands-off approach to the debt talks over the past few weeks.

Perhaps mindful of the long odds of success, Obama has largely left the negotiations alone, after issuing his blueprint in September for more than $3 trillion in savings. “It would be hard [for Obama] to do more. He’s put a proposal down,” lobbyist Steve Elmendorf said. “People know where he stands.”

At the same time, several Democrats said, any greater involvement by Obama at this stage could have a toxic effect as Democrats and Republicans try to find middle ground. If the president were more deeply engaged, it could force Republicans into a reactionary role.

“He doesn’t want to do anything that would detract from getting the votes,” former House Democratic leader Richard A. Gephardt said. Still, Gephardt said, referring to the members of the supercommittee: “If they don’t do anything, then I think the president will try to enter more forcefully.”

With the Nov. 23 deadline looming, it is unclear whether the lawmakers can strike a bargain, and, if they do, whether that deal will pass Congress by the next deadline, Dec. 23.

In a potential preview of how he could respond to anything short of a compromise, Obama has been railing against Congress for its partisan gridlock. At a campaign event in Hawaii on Monday, he made the pitch that “change” takes more than a single presidential term to achieve.

“It’s going to take a few more years to meet the challenges that have been a decade in the making. And I think the American people understand that,” Obama told donors at the Aulani Disney Resort. “What they don’t understand is leaders who refuse to take action. They don’t understand a Congress that can’t seem to move with a sense of urgency about the problems that America is facing.”

Staff writers Felicia Sonmez and Zachary Goldfarb contributed to this report.