An extraordinary bipartisan accord between House Speaker John Boehner and Minority Leader Nancy Pelosi is letting both parties exhale as they move toward permanently ending the nagging annual threat of Medicare cuts to physicians. Yet each side is bragging about more than that.

For Boehner, the package announced Tuesday lets him claim a rare if modest bipartisan pact to strengthen the finances of the costly Medicare health care program for seniors. Attempts by Boehner and President Barack Obama to strike dramatic, money-saving compromises overhauling Medicare and the nation’s other growing benefit programs have foundered in recent years, including during their 2011 “grand bargain” talks.

“We have no intentions of passing any kind of a short-term doc fix. We’ve got a good product, we’re going to pass it here on Thursday and I hope the Senate will move as quickly as possible,” he said, using Washington’s nickname for the Medicare doctors’ measure in a warning to the Senate.

Pelosi, D-Calif., was focused more on the two years of additional money the plan contains for the widely popular Children’s Health Insurance Program and the nation’s community health centers, which serve poor families in every state.

“In this environment I think we made great progress,” said Pelosi, referring to Republican domination of Congress.

The measure would also make permanent programs that help low-income seniors pay Medicare deductibles and poor families retain Medicaid as they get jobs.

Yet Pelosi had to defend the package against Democratic critics, mainly in the Senate, who complained that it doesn’t do enough for children and women and would engrave abortion restrictions into permanent law. The measure subjects community health centers to abortion curbs that Congress has enacted annually since 1979 —called the Hyde amendment — language Pelosi says is routine and will expire after two years.

“I said to my colleagues this morning, I would leave Congress before I’d vote for codification of the Hyde language,” said the 27-year congressional veteran, an abortion-rights leader whose compromise with Boehner is being heavily criticized by normally staunch allies.

House GOP and Democratic leaders said they expected strong support from rank-and-file lawmakers, and House passage seemed likely. Powerful lobbying groups focused their efforts on the Senate, where the American Medical Association has backed the pact while AARP, the senior lobby, has called it “not a balanced deal for older Americans.”

A strong House vote could put extra pressure on the Senate to approve the measure. No. 2 Senate GOP leader John Cornyn of Texas said there was “excitement” among Senate Republicans.

Senate Minority Leader Harry Reid, D-Nev., who has criticized the plan’s abortion restrictions, said he’d wait for House passage “before we start speculating on what we need to do with it, if anything.”

The measure’s main thrust would prevent a scheduled April 1 reimbursement cut of 21 percent for doctors treating Medicare patients. A 1997 budget law pegged the payments to overall economic growth, threatening deep cuts that Congress has blocked temporarily 17 times since 2003.

Sen. Richard Durbin of Illinois, the No. 2 Senate Democratic leader, said Senate action seemed unlikely this week before lawmakers break for a two-week recess. In past stalemates over Medicare reimbursements, the government has delayed paying checks for two weeks while lawmakers settled differences.

Instead of the current reimbursement formula, doctors would get 0.5 percent annual increases for five years. Financial rewards and penalties would be created to coax physicians to bill patients for their quality of care, not the treatments they undergo.