Leading congressional Democrats immediately recoiled Tuesday from a new proposal to cut $600 billion in Medicare spending over the next decade — in part by raising the eligibility age.

Sens. Joseph I. Lieberman (I-Conn.) and Tom Coburn (R-Okla.) unveiled the proposal as part of a bipartisan effort to produce the kind of savings necessary to achieve the $2 trillion in debt reduction both parties say is needed to convince reticent lawmakers to vote to raise the debt ceiling. It would raise Medicare’s eligibility age from 65 to 67 and assess higher premiums on wealthier seniors.

The proposal echoes Republican demands that entitlement reform — especially deep cuts in Medicare spending — be a part of any agreement to raise the nation’s debt ceiling.

But the swift rejection of the proposal among Democrats reflects the significant obstacles that remain to any agreement to cut the deficit and raise the nation’s legal borrowing limit.

Positions on both sides have been hardening in recent days, as an Aug. 2 deadline for working out a deal before the nation defaults on its obligations approaches.

A previously scheduled White House meeting with top Senate Democrats on Wednesday will likely be devoted to the ongoing negotiations.

Republican leaders in the House and Senate have said there can’t be more progress made in negotiations until Democrats agree to entitlement cuts and forgo any new taxes.

Senate Minority Leader Mitch McConnell (R-Ky.), who met with President Obama and Vice President Biden at the White House on Monday, said no additional talks had yet been scheduled.

Democrats insist that the deficit cannot be reduced by cutting spending alone. No deal is possible, they say, without an agreement to close tax loopholes that benefit the wealthy, including subsidies for major oil companies and a tax break provided to companies that buy private jets.

And they have promised they will not trim benefits to Medicare beneficiaries, a point underscored by their chilly reception of the plan advanced by Lieberman and Coburn.

The two senators conceded that their plan would be unpopular but said it presented the prescription to long-term health for the federal program.

“Our plan contains some strong medicine but that’s what it will take to keep Medicare alive. But we believe our plan administers that medicine in a fair way,” Lieberman said. “It asks just about everybody to give something to help preserve Medicare. But it asks wealthier Americans to give more than those who have less.”

With polls showing Medicare cuts deeply unpopular and a restive base anxious that their party may give away too much to achieve a debt deal, Democratic rejection of the proposal was swift.

Senate Majority Leader Harry M. Reid (D-Nev.) termed it “a bad idea.” House Minority Leader Nancy Pelosi (D-Calif.) called it “unacceptable.”

“It is unfair to ask seniors to get less in benefits and wait longer to get onto Medicare — all while Republicans back tax breaks for big oil and corporations that ship American jobs overseas,” Pelosi said.

Economists and credit rating agencies have warned that financial markets may grow turbulent if political leaders cannot show they are making progress toward an agreement to raise the debt limit soon.

For weeks, Biden had been leading a series of closed-door talks with congressional leadership deputies that produced between $500 billion and $1 trillion in agreed upon cuts. But those talks stalled last week after House Majority Leader Eric Cantor (R-Va.) withdrew, citing Democratic insistence on raising taxes.

Now, Obama is working personally to broker agreement on the most difficult issues, including defense spending and entitlement cuts.

But those talks are likely to take place almost entirely in secret, and some rank-and-file Republicans have been smarting over the lack of transparency.

Sen. Ronald H. Johnson (R-Wis.) threatened Tuesday that he would delay further Senate action unless the talks are conducted more openly and Senate Democrats lay out a budget plan. He made good on his pledge late Tuesday, withholding his assent from ending a quorum call to allow a fellow Republican to speak.

“Unless we receive some assurance from the Democrat leadership that we will actually start addressing our budget out in the open, in the bright light of day, I will begin to object” to unanimous consent for business, which would signficantly delay Senate action, he said.