The office of Speaker John Boehner, R-Ohio, released a draft of the resolution that would authorize the House to file suit amid GOP criticism that the president has declined to faithfully execute the laws of the country.
"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 to 99 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.
"I mean, think about that," Obama said Thursday in Austin, Texas, as he criticized Republicans anew. Addressing them, he said: "You're going to use taxpayer money to sue me for doing my job, while you don't do your job."
White House press secretary Josh Earnest reiterated that position and linked it to economic initiatives, saying in a statement that "Republican leaders in Congress are playing Washington politics rather than working with the president on behalf of hardworking Americans."
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.
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.
Obama made light of the calls for impeachment while in Texas. "You hear some of them - 'sue him,' 'impeach him.' Really?" he asked to laughter. "Really? For what?"