Democrats said Obama had acted legally and mocked the case as an unwinnable, politically motivated attack. Legal experts expressed doubts that the GOP would prevail or that the case could be concluded during Obama's presidency.
The suit echoed Republican complaints over Obama's Thursday night announcement of executive actions preventing the deportation of 5 million people who immigrated to the U.S. illegally. GOP lawmakers said those unilateral steps were unconstitutional and have promised unspecified congressional action.
Friday's lawsuit did not address immigration, though a Republican official said party leaders might add that later. The official spoke on condition of anonymity to describe internal Republican deliberations.
House Speaker John Boehner, R-Ohio, said Obama "has chosen to ignore the will of the American people" and cast the battle as one with important implications.
"If this president can get away with making his own laws, future presidents will have the ability to as well," said a Boehner written statement. "The House has an obligation to stand up for the Constitution."
In the past, Republicans have accused Obama of overreaching by trading five Taliban prisoners for captured Army Sergeant Bowe Bergdahl and blocking earlier deportations of immigrant children illegally in the country.
White House spokesman Eric Schultz said the public wants Washington to focus on improving the economy but "Republicans choose to sue us, sue the president for doing his job."
In a written statement, House Minority Leader Nancy Pelosi, D-Calif., called the lawsuit "a bald-faced attempt to achieve what Republicans have been unable to achieve through the political process." She said Republicans were responding to "the howls of impeachment-hungry extremists."
Pelosi also complained that Republicans found "a TV lawyer" who'll cost taxpayers too much — $500 hourly, according to the contract. The lead attorney, George Washington University law professor Jonathan Turley, has done legal commentary on television networks.
Wasting little time, the House Majority PAC, a Democratic campaign committee, blasted a fundraising email to supporters calling the suit "an obvious political stunt to rile up Boehner's Tea Party allies."
Congressional Republicans all opposed the health care overhaul, and the House has voted over 50 times to repeal it.
Friday's suit, filed against the departments of Health and Human Services and the Treasury, was assigned to U.S. District Judge Rosemary Collyer, a 2003 appointee of President George W. Bush.
It accuses Obama of unlawfully delaying the 2010 health care law's requirement that many employers provide health care coverage for workers.
That so-called employer mandate requires companies with 50 or more employees working at least 30 hours weekly to offer health care coverage or pay fines. Smaller businesses are exempt.
The requirement was initially to take effect this year. Now, companies with 50 to 99 employees have until 2016 to comply while bigger firms have until next year.
The suit also accuses Obama of illegally preparing to pay insurance companies an estimated $175 billion over the next decade — plus $3 billion paid this past year —even though Congress hasn't provided money for that purpose.
According to the suit, insurance companies providing coverage under the health law must offer reduced rates to many lower-income policyholders.
The law established a fund to reimburse insurers who do that. Congress hasn't put money into that fund but the administration has started paying insurance companies anyway, the suit says.
University of Richmond law professor Carl Tobias said it would be difficult for the House to prove its case or even get the courts to hear it because of their traditional reluctance to intervene in political disputes between Congress and the president.
Timothy Lewis, a former federal appeals court judge nominated by President George H.W. Bush, said caseloads and potential appeals make it doubtful the case would be finished during Obama's final 26 months in office.
The House authorized the lawsuit in a near party-line vote in July.
AP Special Correspondent David Espo, reporter Donna Cassata and AP White House Correspondent Julie Pace contributed to this report.