Congressional Democrats are urging the debt-reduction supercommittee to pursue a far-reaching agreement to slice $3 trillion from the federal budget over the next decade through significant cuts to federal health programs, including Medicare, and as much as $1.3 trillion in new taxes.

At a closed-door meeting Tuesday, Sen. Max Baucus (D-Mont.) told his colleagues on the panel that they should pick up where President Obama and House Speaker John A. Boehner (R-Ohio) left off in negotiations this summer during a bitter battle to raise the federal debt limit, according to congressional aides in both parties familiar with the meeting. Obama and Boehner were discussing a plan that included provisions to raise taxes, raise the Medicare eligibility age and use a less generous measure of inflation to calculate Social Security benefits.

Speaking on behalf of a majority of Democrats on the panel, Baucus proposed that the committee look at slightly larger revenue increases, the aides said. That idea faced immediate push-back from Republicans on the panel, who have consistently refused to consider raising revenue through any means other than economic growth.

Savings under the plan would be about equally divided between tax increases and spending cuts, including as much as $500 billion in fresh savings from health programs, such as Medicare and Medicaid. Aides said Baucus also urged his colleagues to approve Obama’s request for as much as $300 billion in fresh measures aimed at stimulating the economy, another idea Republicans have resisted.

The offer represents the thinking of Democratic leaders in both chambers, and marks an attempt to jump-start the talks. With a Thanksgiving deadline fast approaching, the two sides have yet to breach the impasse over taxes that has for months stymied ambitious efforts at debt reduction. Boehner twice walked out of negotiations with Obama this summer, blaming differences over taxes.

“This was a good-faith effort to put something on the table to see what kind of response we would get,” said one Democrat familiar with the talks.

Last week, Senate Majority Leader Harry Reid (D-Nev.) broached similar ideas in a meeting with Senate Minority Leader Mitch McConnell (R-Ky.) and House Speaker John A. Boehner (R-Ohio). Democratic leadership aides said the goal was to determine whether a big deal could come together.

Talks have also included a much smaller fallback plan that could come in well under the committee’s goal of $1.2 trillion in savings through 2021.

So far, the response from the GOP has not been favorable. Although they declined to comment publicly on the offer, Republican aides privately dismissed the tax and stimulus pieces as unacceptable.

Republicans also questioned the timing of the offer, which comes nearly two months after the talks began, and suggested that Democrats may be trying to paint themselves as reasonable negotiators, knowing full well that the offer would not fly with the GOP.

“You have to wonder if this is about positioning instead of about moving to resolution,” said Rep. Dave Camp (R-Mich.), a supercommittee member.

The panel has floundered since meetings began in September. If the supercommittee fails to reach agreement to trim borrowing by at least $1.2 trillion through 2021, automatic spending cuts of an equal amount would be triggered in January 2013. These cuts would strike especially hard at the Pentagon, an outcome that Republicans are eager to avoid.

As they headed into a closed door meeting Wednesday afternoon, a number of members of the panel refused to confirm the existence of a Democratic proposal or otherwise comment on the committee’s progress.

“I don’t think it helps our negotiations to be doing it in public,” said Sen. John Kerry (D-Mass.) “I think people know what the issues are and we just need to negotiate them in good faith.”

Kerry would not confirm the existence of a Democratic proposal. Asked if he expected a counterproposal from Republicans on Wednesday, he said, “I’m expecting a negotiation. I’m expect us to negotiate until we don’t negotiate, either because we succeeded or not. One or the other. We have to negotiate. That’s our job.”

Kerry said he continued to believe the committee should strive for the largest deficit reduction package possible.

“I’ve always said I think it’s important that the committee do the most that we can do. I think it’s critical for the country,” Kerry said.

Rep. James E. Clyburn (D-S.C.) laughed when asked about reports of Republican opposition to the proposal but did confirm, as he entered the room, that a Democratic plan existed. “Yeah, I’ve heard of it,” he said.