Top congressional leaders intervened Tuesday in “supercommittee” talks about the national debt, as negotiators faced mounting pressure from both parties to back away from any deal that requires tax increases and cuts to cherished social programs.

With one week remaining before a Thanksgiving deadline, House Speaker John A. Boehner (R-Ohio) and Senate Majority Leader Harry M. Reid (D-Nev.) met briefly to discuss the panel’s deliberations. Aides described the 15-minute session as a “gut check” to determine whether the parties can reach an accord to slice at least $1.2 trillion from projected borrowing over the next decade.

But there was no sign of progress.

And in an evening interview on CNBC, Jeb Hensarling (R-Tex.), the panel’s House co-chairman, said that the group’s Republican members have “gone as far as we feel we can go” on the key issue of taxes.

Democrats quickly pounced on the implication that Republicans were backing away from the bargaining table.

“It looks like these guys are giving up and throwing in the towel,” said Rep. Chris Van Hollen (Md.), who has been at the center of the negotiations. The latest GOP offer “does not meet the test of a balanced approach,” he added.

In recent days, talks have focused on a tax package of as much as $650 billion over the next decade, with $100 billion in upfront tax increases on various business interests and $550 billion to come later through an overhaul of the tax code, according to sources in both parties with knowledge of the discussions.

But on Tuesday, it was unclear whether either side could make those numbers work. Such a deal probably would require far deeper cuts to entitlements than most Democrats have been willing to stomach. Meanwhile, some Republicans are drawing a hard line at the $300 billion in new taxes in the most recent GOP offer.

By early evening, Reid, Senate Minority Leader Mitch McConnell (R-Ky.) and their top policy aides had all left the Capitol, a stark contrast from the round-the-clock negotiations that marked the summer negotiations.

Reid told reporters earlier in the day that he had hoped that by now “there would be a lot of hand-holding and hugs and pats on the back and we’d be headed home for Thanksgiving.”

Instead, the talks have included “a few armlocks” and “headlocks,” Reid said, adding: “I hope we can get this done.”

While Democrats and Republicans on the supercommittee huddled separately Tuesday, the clamor against a bipartisan deal continued to grow.

The process remains stymied by the same issues that killed the chance of major compromise during the summer debt-ceiling debate.

Some conservatives in the Republican House majority said they could not support the latest GOP offer to raise taxes by as much as $300 billion over the next decade as part of a broader deal to cut spending. The offer marked the first time Republicans other than Boehner have proposed raising taxes above current levels.

Liberal lawmakers and progressive groups have been equally dismayed by the prospect that Democrats on the supercommittee may be willing to accept sharp cuts in domestic programs, including Medicare and Medicaid, in exchange for a relatively minor increase in taxes.

“I hope they don’t get a deal,” said Rep. Jerrold Nadler (D-N.Y.), arguing that any agreement to cut spending would only deepen an unemployment crisis that he likened to the Great Depression.

Even as supercommittee members struggled to chart a path to a compromise that would not alienate their respective political bases, a bipartisan group of lawmakers from the House and the Senate planned to renew a call Wednesday for the panel to pursue a more ambitious deal that would require major surgery to Medicare, Medicaid and Social Security, as well as historic tax increases.

“I fear it will take a miracle,” said Rep. Jim Cooper (D-Tenn.), a moderate who has long urged far-reaching action to tame the debt. Extremists in both parties have sent up “battle cries,” he said, summoning their troops to attack even the modest concessions that have leaked from the panel’s secret negotiations.

In an offer last week, Republicans proposed an overhaul of the tax code that would lower rates but limit or eliminate dozens of credits and deductions — resulting, they said, in about $300 billion in fresh tax revenue over the next decade. Democrats rejected the offer, which also called for lowering the top income tax rate to 28 percent, arguing that the GOP approach would result in more tax cuts for the wealthy and tax increases for the middle class.

But the mere discussion of higher revenue has anti-tax Republicans deeply nervous.

“We said ‘no new taxes.’ This looks to me like new taxes,” said Rep. Steve King (Iowa).

“Emotionally, I’m certainly not there,” added Rep. Michael C. Burgess (Tex.). Asked what would persuade him to sign on to a final deal that includes higher taxes, he responded: “Short of pestilence, famine and the end of the world?”

On Tuesday, Reid accused Republicans of taking their cues from GOP strategist Grover Norquist, who crafted the anti-tax pledge that virtually every Republican in Congress has signed. In an interview, Norquist said that Republicans have no intention of raising taxes, and that their decision to show “a little ankle” on taxes in their latest offer was merely a ploy to prove that Democrats would not endorse structural changes to Medicare and Medicaid.

Norquist acknowledged that the GOP tax plan is “problematic,” however, and said he would have pushed Republicans to rescind the offer if Democrats had accepted it. Jeb Hensarling

And if Republican supercommittee members did agree to a deal to raise taxes, Norquist said, he is confident that Republican House members would reject it.

“Three guys suffering Stockholm syndrome because they’ve spent too much time caucusing with Democrats are not going to get Republicans to break the pledges they’ve made to their constituents,” Norquist said.

But Hensarling appeared to win over some of the chamber’s most conservative members in a closed-door presentation Tuesday.

Afterward, Boehner told reporters that “I’m convinced that if, in fact, there is an agreement, that it can, in fact, pass” the House.

Under legislation approved during the summer debt-limit debate, any agreement that emerges from the supercommittee would go straight to the House and Senate floor and would be protected from both filibuster and amendment. The panel has until Nov. 23 to strike a deal and Congress has until Dec. 23 to pass it. Failure on either would trigger $1.2 trillion in automatic cuts to agency budgets over the next decade, beginning in January 2013.

The panel’s Democrats, meanwhile, face pressures of their own. Offers advanced by Democrats have included significant cuts to Medicare, Medicaid and domestic agencies, deeply upsetting liberal groups. Anxiety is also building over the possibility that the supercommittee could cut spending immediately, but leave until next year an overhaul of the tax code that would raise new revenue.

Two Democrats on the supercommittee have signaled their displeasure. Rep. James E. Clyburn (S.C.) said Sunday that the six Democrats on the panel had yet to “coalesce” behind a plan. Rep. Xavier Becerra (Calif.) said the same Tuesday.

“Is there a plan that has actually been presented to the Republicans as the six members on the Democratic side?” he said, adding that “conversations” are still ongoing.

On Thursday, the group Move­ plans to join other progressive groups in staging protests nationwide to pressure supercommittee Democrats.

“Nobody’s happy with the offers the Democrats are putting on the table,” said Daniel Mintz, the group’s campaign director. “Any Democrat who signs off on a deal like those are imperiling their political futures.”

Staff writers David A. Fahrenthold, Felicia Sonmez and Paul Kane contributed to this report.