Sens. Joe Lieberman (I-Conn.) and Tom Coburn (R-Okla.) entered the debt and deficit debate Tuesday, proposing a Medicare overhaul they said would cut the deficit by about $600 billion during the next decade.

The duo, which Coburn nicknamed the “brothers two,” now intends to drum up support by shopping its plan around, including to the “gang of six,” from which Coburn took a sabbatical. Coburn left the bipartisan group, which was exploring ways to decrease the deficit, because he felt it was not going far enough in cutting entitlements.

But he has clearly found an ally in Lieberman, who in recent years has leaned more to the right on health care issues despite remaining a member of the Democratic Conference.

Under their plan, the age of eligibility for Medicare would gradually increase to 67 from 65, starting in 2014. The proposal assumes the continued implementation of President Barack Obama’s health care law. Under the Coburn-Lieberman plan, seniors would be eligible to participant in the health care exchanges created by that law.

The proposal would gradually increase premiums paid by all seniors to generate the bulk of the savings. It would also require wealthier seniors to pay much higher premiums.

Lieberman, who had wanted a 1 percent income tax hike on people making more than $250,000 a year, said he compromised that away in return for having wealthier people pay more for their Medicare.

At a press conference, both Senators said Medicare and the nation are headed for a fiscal cliff. “The sooner you take the strong medicine, the sooner you’ll get healthy again,” Lieberman said.

“Nobody’s going to like this plan, we understand that,” Coburn said. But he said that without action, Medicare is going to change anyway because the country won’t be able to borrow enough to pay for it.

The new proposal also includes one provision that might be attractive to other Democrats — a $7,500 yearly out-of-pocket cap to protect seniors from catastrophic costs. That cap rises for higher-income seniors.

Top Democrats, however, have made it clear they will not support a major overhaul of Medicare without tax revenues and will not support cutting benefits themselves under any scenario.