Correction: An earlier version of this story misattributed a comment about a House bipartisan letter to Rep. Jon Runyan (R-N.J.) The comment was made by Rep. Thomas J. Rooney (R-Fla.) The story has been corrected.

With a Thanksgiving deadline fast approaching, a special debt-reduction committee is suddenly springing to life on Capitol Hill.

Democrats made the first move in a closed-door meeting this week, pressing the bipartisan panel to pursue a far-reaching deal to slice $3 trillion from the federal budget over the next decade through an equal mix of spending cuts and new revenue. The proposal calls for significant cuts to health and retirement programs, as well as $1.3 trillion in new taxes.

Speaking for a majority of the six Democrats on the panel, Sen. Max Baucus (Mont.) on Tuesday urged his GOP colleagues to pick up where President Obama and House Speaker John A. Boehner (R-Ohio) left off in a summer battle over raising the federal debt limit.

Baucus, who chairs the Senate Finance Committee, offered to cut as much as $500 billion from Medicare and other health programs and to adopt a less generous measure of inflation to calculate Social Security benefits, according to aides familiar with the talks. He also called for as much as $300 billion in new measures aimed at stimulating the flagging economy.

Republicans quickly rejected that offer. Senior aides called the tax and stimulus provisions un­acceptable. The GOP countered Wednesday with its own plan to tame the debt without raising taxes, leaving the two sides apparently stuck on the same issues that have stymied action for months.

But after weeks of aimless floundering by the “supercommittee,” the exchange marked the beginning of a more serious phase that will determine whether lawmakers can break that political impasse.

Neither side seemed certain where the path would lead. Republicans questioned the timing of the Democratic offer, which came nearly two months after the talks began. Some suggested that Democrats were trying to paint themselves as reasonable negotiators in anticipation that the talks will ultimately fail.

“You have to wonder if this is about positioning instead of about moving to resolution,” said Rep. Dave Camp (R-Mich.), a panel member who chairs the House Ways and Means Committee.

Senate Majority Leader Harry M. Reid (D-Nev.) broached the idea of a “grand bargain” on taxes and entitlements in a meeting last week with Boehner and Senate Minority Leader Mitch McConnell (R-Ky.). Democratic leadership aides said the goal was to determine whether such a deal could come together.

“This was a good-faith effort to put something on the table to see what kind of response we would get,” said one senior Democrat, speaking on the condition of anonymity to discuss the private talks.

But Boehner and McConnell have been steadfast in their refusal to consider tax increases big enough to persuade Democrats to throw their weight behind reductions to popular social programs.

“Their offer is a joke,” said one Democrat with knowledge of the GOP counter-proposal. “Democrats came to the table with an offer that had serious skin in the game for both parties. Rather than offering real solutions, Republicans are just doing more of the same posturing they do every time they walk away from efforts to constructively tackle this crisis.”

Aides in both parties said Wednesday that they are not optimistic about the prospect of a major breakthrough. So congressional leaders are discussing a fallback plan in the range of the committee’s original goal of at least $1.2 trillion in savings through 2021.

Still, support for a bigger deal appears to be on the rise. With a new CBS-New York Times poll showing public approval for Congress hovering at 9 percent, a bipartisan group of House members circulated a letter Wednesday aimed at pumping up the supercommittee’s ambitions.

“We’re trying to give them a shot in the arm,” said Rep. Mike Simpson (Idaho), an author of the letter who was urging fellow Republicans to sign on. “The supercommittee needs to go big,” he said, and “everything needs to be on the table,” including revenue, or higher taxes.

Rep. Thomas J. Rooney (R-Fla.), who signed the letter, said organizers hoped to get as many as 100 signatures. “The goal is to take this opportunity to show the American people this Congress can function in a bipartisan way and can get the things done that the people expect us to get done, so our approval rating gets a little better than the 9 percent we’re evidently at now,” he said.

The supercommittee was created in the aftermath of the debt-limit debate, when the partisan battle over spending drove the nation to the brink of default, threatening the fragile economic recovery. Public faith in government collapsed, even as lawmakers agreed to cut $900 billion from agency budgets over the next decade and assigned the panel to find additional savings.

The panel faces a Nov. 23 deadline to agree on a debt-reduction plan that would move through Congress with special procedural protections against any amendment or filibuster in the Senate. If the committee’s mission fails, across-the-board reductions will be triggered in January 2013.

Those cuts would fall heavily on the Pentagon, so Republicans are feeling pressure to seek a compromise to avoid them. On Wednesday, during the supercommittee’s fourth public hearing, Douglas W. Elmendorf, director of the nonpartisan Congressional Budget Office, said defense spending would fall $110 billion short of keeping pace with inflation by 2021.

The trigger would endanger other fast-growing programs, he said, such as health care for veterans and Pell grants for college students.

Lawmakers who hoped to count savings from the wind-down of the wars in Iraq and Afghanistan toward the debt-reduction target were met with bad news. The White House has estimated that such savings could amount to more than $1 trillion over the next decade. But because war spending has already started to fall, the CBO has adjusted its estimates, Elmendorf said. War savings are now likely to contribute no more than $700 billion toward the committee’s goal.

In her opening statement, Sen. Patty Murray (Wash.), the Democratic co-chairman of the panel, tried to reassure those who have been alarmed by the appearance of a stalemate.

“We aren’t there yet, but I am confident that we are making progress,” she said. “And I’m hopeful that we’re moving quickly enough to meet our rapidly approaching deadline.”

Later in the day, as the panel headed into another closed-door session, Sen. John F. Kerry (D-Mass.) said the group will “negotiate until we don’t negotiate, either because we succeeded or not. One or the other. We have to negotiate. That’s our job.”