WASHINGTON (AP) — An uncharacteristic joint effort by House Speaker John Boehner and his usual nemesis, Minority Leader Nancy Pelosi, to resolve a gnawing problem about how Medicare pays doctors underscores the political victories each sees in finally sweeping the issue off the deck — if they can.

Boehner, R-Ohio, has taken the unusual step of working with Pelosi toward a compromise both leaders are shopping to lawmakers. This is angering some conservatives with whom he's repeatedly clashed, including last month when they opposed legislation preventing a Homeland Security Department shutdown and he turned to Pelosi, D-Calif., for votes.

Pelosi knows many liberals are unhappy that the proposal would increase costs for some Medicare beneficiaries, but not for the doctors who would benefit.

Both leaders think the clashes are worthwhile for a proposal that would block an April 1 cut of 21 percent in Medicare fees for physicians, revamp how they're paid and replenish money for a popular children's health program.

WHAT'S THE PROBLEM?

A 1997 budget deal included a formula limiting physicians' reimbursements for Medicare patients. Because medical costs have grown faster than envisioned, that formula requires fees that legislators consider unrealistically low and doctors warn could make them abandon Medicare recipients.

Congress has blocked the cuts 17 times since 2002. That has meant recurrent battles over finding budget cuts to replace the lost savings, fights many lawmakers want to end.

WHAT WOULD BOEHNER AND PELOSI DO?

Top lawmakers introduced legislation Thursday that would abolish the existing doctors' fee formula and grant physicians 0.5 percent annual increases for five years. Hoping to curb Medicare spending, doctors would be offered financial incentives to charge patients for the quality of care they receive, not the treatments they undergo.

Leaders were still completing the rest of the package as they hunted votes. Lawmakers, lobbyists and aides say it would also finance the Children's Health Insurance Program, serving around 8 million low-income children annually, for two more years, and provide money for community health centers.

Overall, the changes would cost roughly $200 billion over 10 years. About $140 billion would be financed with bigger federal deficits, the rest split between higher costs for some Medicare recipients and cuts to providers like nursing homes.

The proposal's fate is unclear, especially in the Senate, a bystander in the process.

WHAT'S IN IT FOR BOEHNER?

Resolving the perennial conundrum over physicians' Medicare fees could show voters the Republican-run Congress can govern while simultaneously averting another self-inflicted crisis. That's important with the 2016 presidential and congressional campaigns looming.

The proposal's higher premiums for top-earning Medicare recipients, plus increased costs for people buying Medigap policies, could let Boehner claim to have reformed the costly Medicare program, another Republican goal. Boehner would resolve the problem without tax increases, a GOP priority.

Fixing the fee problem would please the medical industry, whose campaign contributions lean Republican.

WON'T BOEHNER BE HURT BY ANGERING CONSERVATIVES?

Some conservatives oppose the plan because it would increase deficits over the coming decade. They also resent Boehner's cooperation with Democrats.

"We all got elected to push conservative policies, not sit down with Nancy Pelosi and work out something," said Rep. Tim Huelskamp, R-Kan.

Some Republicans say if Boehner can't win over conservatives on bills he considers crucial, why not start by seeking Democratic votes?

"It sends a message to the caucus: 'Guys, if you don't work with me to get this stuff done, we're going to get it done another way,'" said former Rep. Tom Davis, R-Va., a GOP insider.

DO ALL CONSERVATIVES OPPOSE THE DEAL?

Many support it, citing Republican projections that charging the wealthiest Medicare recipients higher premiums would reap billions over two decades. They say a deal would clear the way for a future Medicare overhaul.

WHAT DOES PELOSI ACHIEVE?

Ending persistent doubts about doctors dropping Medicare is a plus for both parties, which compete for support from heavy-voting seniors. Democrats are especially protective of Medicare and consider stabilizing it a victory.

Many Democrats are pleased that to pay for the $200 billion plan, benefit cuts are relatively small. According to one Democratic aide, of roughly $35 billion in pared benefits, all but $1 billion comes from higher Medicare premiums for people earning more than $133,000 yearly. Liberals worry the increase might eventually spread to lower earners.

A program helping low earners pay Medicare costs like deductibles would become permanent, another Democratic win.

The children's health program, whose funding expires Oct. 1, would be financed two more years. Democrats consider that a victory, though Democratic senators and liberals want four years.

Locking that children's money down avoids leaving it vulnerable to a Supreme Court case later this year. If the justices invalidate subsidies under President Barack Obama's health care overhaul, the children's program could become a bargaining chip in negotiations with Republicans to rebuild that law.