WASHINGTON–Here’s a political pitch you don’t hear too often: “Nobody’s going to like this plan. We understand that.”

That’s how Sen. Tom Coburn, a hard-edged fiscal conservative from Oklahoma, described the Medicare reform proposal he’s been working on with Sen. Joseph Lieberman, a Connecticut independent.

The two senators fleshed out their controversial plan at a much-touted news conference Tuesday, saying it would save $600 billion over ten years, extend the solvency of the program by about 30 years, and serve as a “bipartisan beachhead” in what has so far been a charged, politically-divisive debate.

And although the plan is still likely to generate stiff opposition, at least two new elements of the proposal, hashed out in quiet negotiations between Lieberman and Coburn in recent days, could make it more attractive.

The two lawmakers added a provision that would stave off, for the next three years, steep scheduled payment cuts to doctors who treat Medicare patients, a major headache that Congress grapples with every year but has been unable to fully resolve. And they removed a 1 percent tax hike on wealthy Americans-a new revenue stream that Lieberman had wanted to dedicate to Medicare to shore up the program, but that would have made his bill a non-starter with congressional Republicans.

“Our plan contains some strong medicine,” Lieberman said at the news conference, “but that’s what it will take to keep Medicare alive.”

Instead of a tax hike, the two senators agreed to include so-called “means-testing” in the plan, which would require wealthier Medicare beneficiaries to pay more for their care than low and middle-income participants. For example, the proposal would require enrollees who make more than $150,000 a year, or $300,000 for couples, to pay their entire premium of $400 a month or more.

People in that income bracket would also have to pay more for their prescription drugs. And they’d face a higher cap on their maximum annual out-of-pocket costs. For example, an individual making less than $107,000 a year would pay up to $12,500 out of pocket per year under the Lieberman-Coburn proposal, while someone making more than $163,000 a year would pay $22,500.

“He gave up something,” Coburn said of Lieberman’s proposed tax hike, which the Connecticut lawmaker had included in an initial outline earlier this month. “I gave up significant things,”

To be sure, means testing is not an idea Republicans generally embrace. But in this case, it was more palatable to Coburn than a tax increase, which would have made the measure dead-on-arrival anyway.

The Medicare reimbursement fix would cost $40 billion over three years, to be paid for by other provisions in the bill. And it could generate significant interest among lawmakers searching for a solution to that perennial problem; the reimbursement cuts have caused deep angst among doctors who have stopped, or threatened to stop, taking Medicare patients because the cuts would deal a major financial blow to their medical practices.

Lieberman saw Coburn as an appealing co-sponsor for his Medicare plan in large part because of the Oklahoma Republican’s fiscal bona fides. Coburn has led the charge in the Senate against what he sees as wasteful Washington spending, whether it’s earmarks or ethanol subsidies. Since Coburn’s hallmark issue is deficit reduction, Lieberman’s aides hope that he will give some momentum to the Medicare proposal as policymakers look for ways to rein in federal spending.

Aside from those two new provisions, however, the measure still includes many deeply contentious ideas. It would, for example, gradually raise the Medicare enrollment age, now set at 65, starting in 2014; by 2025, the elderly would have to wait until they turn 67 to be eligible for the government health insurance program.

It would also increase premiums for all beneficiaries and add new co-pays for home health care services, lab work, and skilled nursing care.

As a result of those and other provisions, Democrats and some outside advocacy groups have blasted the plan. House Democratic Leader Nancy Pelosi called it “unacceptable” in a tweet on Tuesday.

“It’s a step up from dreadful,” said Judith Stein, executive director of the Center for Medicare Advocacy, a Connecticut-based organization. “It’s better than eliminating the program,” she added, a reference to the House GOP plan to turn Medicare into a private, voucher-based system.

She said in drafting their proposal, Lieberman and Coburn ignored several major steps that could shore up Medicare without undermining benefits or reducing access to the program. Instead of raising the eligibility age, she said, lawmakers should lower it to 55, letting younger individuals buy into the program.

“People would pay for it and put money into the system when they are younger and less likely to use the services,” she said. “It would give more revenue to the program… and the risk pool would be enlarged.”

She also noted that they took off the table the idea of allowing Medicare officials negotiate with pharmaceutical companies over drug prices, which could save billions of dollars a year. Lieberman said at the press conference that he was open to that idea, but it’s been strongly opposed by Republicans.

Stein said other elements of the bill, such as the means testing and increased co-pays and premiums, could end up causing wealthier elderly patients to drop out of Medicare in favor of private insurance, making the program less viable and attractive to those left.

Similarly, the AARP’s executive vice president, Nancy LeaMond, said in a statement that her group had “serious concerns” with the proposal. She said it “relies almost entirely on shifting costs and removing coverage for seniors who depend on Medicare as a lifeline.”

She said AARP “will continue our efforts to protect Medicare from harmful cuts as part of a deal to pay the nation’s bills.”

Stein said she wasn’t sure if the Lieberman-Coburn plan could gain political traction or not. “But clearly having what, at least on paper, is a viable bipartisan bill means that it’s going to be paid attention to,” she said.

And in fact, Tuesday’s news conference was a standing-room only affair; when it was over, reporters trailed Coburn and Lieberman down the hall, asking more questions, until they disappeared into an elevator.

While Democrats rejected it out of hand, Republicans were not so dismissive.

The Senate’s top Republican leader, Mitch McConnell of Kentucky, did not delve into the details of the proposal or take a position on it Tuesday. But he said it was at least a good sign that two political opposites had teamed up to offer “something serious” on entitlement reform.

“We can put our heads in the sand and ignore [the problem of Medicare’s increasing costs] and keep on kicking the can down the road,” McConnell said, “or we can come together, as Sen. Coburn and Sen. Lieberman have, and … try to do something about it.”