"In 2013, the president changed the health care law without a vote of Congress, effectively creating his own law by literally waiving the employer mandate and the penalties for failing to comply with it," Boehner said in a statement. "That's not the way our system of government was designed to work. No president should have the power to make laws on his or her own."
The so-called employer mandate was written into the law as a guardrail to discourage employers from shifting workers into taxpayer-subsidized coverage. Under those rules, companies with 50 or more workers must provide coverage or pay a $2,000-per-worker fine.
The administration gave businesses an extra year to comply with the health care law's requirement to offer coverage.
The House Rules Committee has scheduled a hearing on the resolution next week, with a House vote later this month.
Obama has called the GOP effort a "stunt" and criticized lawmakers for inaction on legislation such as a stalled bill to overhaul the nation's immigration system.
Drew Hammill, a spokesman for Democratic leader Nancy Pelosi, said the effort was a waste of taxpayer dollars.
"This lawsuit is just another distraction from House Republicans desperate to distract the American people from their own spectacular obstruction and dysfunction," Hamill said. "Congress should be creating jobs, raising new ladders of opportunity, and focusing on the challenges facing hard working American families."
Boehner's actions on the lawsuit come as some Republicans are demanding a far more formidable step—impeachment.
Former vice presidential candidate Sarah Palin and others have called for Obama's impeachment. Boehner said Thursday that he disagrees with those calls, but asserts that others can make a determination on their own whether the chief executive deserves it.
This article has been updated to indicate that companies with 50 or more workers must provide coverage or pay a $2,000-per-worker fine.