Correction: An earlier version of this article incorrectly included Senate Finance Committee Chairman Max Baucus (D-Mont.) among those who talked privately with Bowles afterward. Bowles met briefly with two other supercommittee members, but he did not meet with Baucus. This version has been corrected.

Erskine Bowles, the former White House chief of staff who has worked for months to tame the national debt, bluntly warned members of a congressional panel Tuesday that they will “fail the country” if they do not break the impasse over taxes that is blocking a far-reaching agreement.

“I know most of you. . . . I have great respect for each of you individually,” Bowles told the 12 lawmakers gathered before him in an ornate House hearing room for the fifth public meeting of the debt-reduction supercommittee. “But collectively, I’m worried you’re going to fail. Fail the country.”

Bowles then surprised the committee by laying out a path to compromise that would split the difference between the competing debt-reduction proposals each side offered last week. He challenged Democrats to accept deeper cuts to federal health programs and Republicans to embrace $800 billion in new taxes, as House Speaker John A. Boehner (R-Ohio) did during this summer’s negotiations over the federal debt limit.

Added to previous budget cuts, such a deal would slice $3.9 trillion from projected borrowing over the next decade, Bowles said, stabilize the debt as a percentage of the economy, and avert a “disastrous” failure of leadership that would undermine the nation’s global standing and lead investors to “look at this country and say, ‘You guys can’t govern.’ ”

“You all know what we have to do,” added Republican former senator Alan Simpson (Wyo.), who served with Bowles, a Democrat, as co-chairmen of President Obama’s fiscal commission last year. “In your gut, you know what we have to do.”

Testifying with Bowles and Simpson at Tuesday’s hearing were the former co-chairs of a separate debt-reduction panel, former Clinton White House budget director Alice Rivlin and former senator Pete Domenici (R-N.M.). All four urged the supercommittee members to set aside their differences on taxes and entitlements and craft a plan that would achieve as much as $4 trillion in savings, warning that nothing less than the country’s economic future is at stake.

“It was helpful, but we have some tough decisions to make,” House Ways and Means Committee Chairman Dave Camp (R-Mich.) said of the day’s testimony.

Others were unimpressed by Bowles’s offer of help and by his public assessment that the supercommittee is failing in its assignment to come up with a blueprint for cutting at least $1.2 trillion from deficits over the next decade.

Rep. Jeb Hensarling (R-Tex.), the supercommittee co-chairman, noted that Bowles’s plan “certainly created some excitement with the press.” But he cautioned Bowles: “Don’t necessarily believe everything you read and hear about the work of this committee.”

With barely three weeks remaining until the committee’s Thanksgiving deadline, there has been little outward sign of progress. Members of the panel and senior aides said the two sides remain deadlocked over the issue of taxes, with Democrats unwilling to accept significant cuts to health and retirement programs unless Republicans assent to billions of dollars in fresh revenue over the next decade.

Various subgroups of the supercommittee have been meeting for weeks to try to forge a compromise, aides and members said, looking for agreement on a deal that ranges from $1.2 trillion to as much as $4 trillion. Portman, Sens. John F. Kerry (D-Mass.) and Patrick J. Toomey (R-Pa.), and Rep. Chris Van Hollen (D-Md.), for example, have met several times to swap ideas. More recently, Camp, Baucus and House Energy and Commerce Committee Chairman Fred Upton (R-Mich.) met with Portman, Kerry and Van Hollen.

But those familiar with the meetings say they have made almost no headway, given the refusal of Boehner and other GOP leaders to accept tax increases except through economic growth. “Meeting does not equal progress,” one Democrat said.

“This has always been a long shot that they could go big and go bold and be smart,” Bowles said in an interview after the hearing.

“Would I bet the ranch on it? No,” he said. “But it’s worth working on it, and that’s what I’m doing.”

Staff writer Felicia Sonmez contributed to this report.