WASHINGTON — In uncommon bipartisan harmony, the House approved a $214 billion bill on Thursday permanently blocking physician Medicare cuts, moving Congress closer to resolving a problem that has plagued it for years.

The lopsided 392-37 vote shifted pressure onto the Senate, where its prospects have brightened as Democrats have muffled their criticism and President Barack Obama has embraced the bill. But with some conservatives also balking at the legislation, its fate there remained murky.

Thursday’s House vote came on a package that bore victories for Republicans and Democrats alike and was negotiated by the chamber’s two chief antagonists, Speaker John Boehner and Minority Leader Nancy Pelosi. That unity contrasted vividly with the usual partisan duels that hamper most congressional efforts on budget, health and other major policies.

The vote even gave House GOP leaders a respite from the large-scale rebellions they frequently face from tea party conservatives, including on a measure last month that prevented a Homeland Security Department shutdown. Republicans backed the Medicare bill 212-33, while Democrats tilted “yes” by 180-4.

“I want to give John Boehner and Nancy Pelosi credit,” said Obama while visiting Birmingham, Alabama. “They did good work today.”

The bill contains funds for health care programs for children and low-income people that Democrats touted as victories. Republicans won long-term though modest strengthening of Medicare’s finances, including cost increases for higher-income recipients.

Buoyed by such incentives, House members more accustomed to gridlock found themselves with little to argue about. Instead, they praised the bill and each other — one Republican even wished Pelosi, D-Calif., a happy birthday, her 75th — as they all but marveled at their unity in addressing a problem.

“I just want to say to the American people, don’t look now but we’re actually governing,” said Rep. Renee Ellmers, R-N.C.

Congress planned to leave town by week’s end for a spring break, and physicians treating Medicare patients face a 21 percent fee cut on April 1 unless lawmakers act. If the Senate doesn’t give final approval before recessing, the government could delay processing doctors’ Medicare checks until lawmakers return to the Capitol.

Underscoring dissatisfaction by some conservatives, Sen. Ben Sasse, R-Neb., said the bill would deepen budget deficits and barely strengthen Medicare, adding, “We should use this crisis as an occasion to be talking about real entitlement reform.”

Physician groups have long warned that the constant procession of threatened slashes in Medicare payments could mean fewer doctors would treat the program’s elderly recipients.

The American Medical Association and other medical organizations urged the Senate to act quickly, saying it would have “a real and lasting impact” on patients and doctors’ practices. AARP, the seniors’ lobby, criticized the higher costs the legislation would mean for Medicare beneficiaries and offered to help the Senate “improve this important bill.”

“This is what we can accomplish when we’re focused on finding common ground,” said Boehner, R-Ohio. He said Republicans would continue pushing to tighten the finances of Medicare and other costly benefit programs, a battle that has produced stalemates with Obama for years.