House Speaker John Boehner floated the lawsuit idea Tuesday, in a private meeting with GOP lawmakers.

At this stage, the legal option is only being discussed, and no timetable has been set. Options include joining a lawsuit already filed by states over the issue, or filing a separate lawsuit.

But the idea quickly became fodder for Democrats, who accused the other side of turning Congress into a "circus."

"Once again, House Republicans are crawling to the courts to relieve them of their responsibility to govern," Drew Hammill, spokesman for House Democratic Leader Nancy Pelosi, said in a statement. "Republicans should stop wasting millions of taxpayer dollars suing the President, and start showing some seriousness for the security of the American people." 

The lawsuit option, though, could be a backup plan for GOP leaders, who want to see what happens with a House-passed bill that would overturn Obama's immigration actions -- which lifted the threat of deportation for millions of people here illegally.

Senate Majority Leader Mitch McConnell has promised a vote on the House-passed bill, and said Tuesday that the Senate would take up the issue after completing consideration of the Keystone XL oil pipeline, which could be as soon as next week.

But Senate Republicans could have a tough time passing the measure, which was added to must-pass legislation to fund the Department of Homeland Security beyond February.

It's not clear how that issue will be resolved. "At this point it's up to the Senate to act, and I expect that they will soon," Boehner told reporters Tuesday.

If that bill dies in the Senate, House GOP leaders may turn to the lawsuit option instead. House Republicans already have sued to try to challenge unilateral changes Obama made to his health care law.

Boehner spokesman Michael Steel said, "Congress will continue to fight for the Constitution, and against the president's efforts to unilaterally re-write his health care law, which is raising costs and costing jobs."

The uncertainty has frustrated conservative Republicans who believe Congress' top priority on immigration should be to hold firm against Obama. They united against a separate border security bill that was scheduled to come to a vote on the House floor Wednesday, and GOP leaders delayed action, citing changes to the House schedule caused by the inclement weather. It's not clear when that bill might come back up.

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