House Speaker John A. Boehner has hinted at a lawsuit to stop President Obama’s nuclear deal with Iran, but legal analysts doubted such a move would work, saying it’s exactly the kind of case judges will steer clear of.

It’s not even clear who, exactly, would even be able to show they have standing to sue — and unless someone can prove an injury, Mr. Obama is likely to have a free hand to lift sanctions on his own timetable.

“It’s hard to see who would,” said Stephen I. Vladeck, a professor at American University’s Washington College of Law who specializes in national security law. “This is the exact kind of dispute that has historically been left to the political branches to work out between themselves.”

Republicans are desperate to find a way to stop the Iran deal, but saw their legislative options narrowed last week after Senate Democrats mounted a filibuster to sustain the deal. That’s led some Republicans to look hopefully to the courts.

“That is an option that is very possible,” Mr. Boehner, Ohio Republican, said last week.

There are two potential avenues of lawsuit. One, a constitutional challenge, would involve challenging the deal as a treaty, which would mean it would take a two-thirds affirmative vote of the Senate to ratify it, rather than the reverse two-thirds votes in both chambers to disapprove it — the system Congress laid out for the Iran deal.

Mr. Vladeck said, however, that the U.S. Supreme Court for decades has held that not all foreign policy deals are treaties, even if the Senate disagrees. And in this case, the Senate took a vote earlier this year that rejected the idea it was a treaty.

Another lawsuit possibility would stem from the law Congress passed and Mr. Obama signed earlier this year governing how the president could go about lifting sanctions on Iran. Under the Iran Nuclear Agreement Review Act, Mr. Obama is required to submit all of the deal’s paperwork to Congress, starting a 60-day review period, and only then can he cancel economic sanctions.

Republicans argue the president has withheld some of the key agreements on monitoring between Iran and the International Atomic Energy Agency, asserting that means the 60-day review hasn’t started and so the sanctions can’t be lifted.

The House voted along party lines last week to declare the president broke the review act, sparking Mr. Boehner’s intimating that a lawsuit is possible.

Senate Majority Leader Mitch McConnell, however, has made no moves to follow the House’s lead, undercutting the strategy’s effectiveness.

House Republicans may be feeling emboldened by last week’s federal court ruling that the House had standing to sue over how Mr. Obama carried out the Affordable Care Act, spending money on something that Congress had specifically forbidden.

But the Obama administration has vowed to appeal, and legal analysts say the House will have a tough time proving its case.

Still, the power of the purse remains a critical congressional weapon, and Congress could use it in the case of Iran.

Mr. Boehner raised that possibility last week, too.

House Republicans have threatened to use the tactic over the last five years on everything from Obamacare to the president’s immigration actions to taxpayer funding for Planned Parenthood — all without success.

Senate GOP aides said the issue hasn’t been raised on their side of the Capitol.

For its part, the White House mocked the idea of a lawsuit, calling it “the Tortilla Coast gambit,” in reference to a popular restaurant and drinking spot near the House office buildings and the Republican National Committee headquarters.

“Like many decisions that are made, probably, on Tuesday night at Tortilla Coast, they seem like a great idea after a couple of margaritas, but when faced with the scrutiny of the light of day, they don’t seem quite as realistic,” White House press secretary Josh Earnest said.

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