By Jake Sherman and Lauren French

There is no shortage of actions that House Republicans see as illegal overreach by President Barack Obama.

They were furious when he bypassed Congress to swap Guantánamo Bay detainees for an American prisoner of war. They were angry when he tweaked immigration law without congressional approval. They considered taking him to court for both.

But instead of a multipronged legal assault against the Obama White House in the middle of an election year, Speaker John Boehner is training his fire on the issue that has most animated the GOP since it took control of the House in 2011: Obamacare. Republicans are betting they can translate their success in making the law politically potent into a legal victory.

The lawsuit — which will have its first congressional hearing Wednesday — is based entirely on Obama’s decision to delay a mandate in the health care overhaul that most employers provide health insurance to workers.

The decision to focus on Obamacare was surprising to some who expected a more sweeping legal action. But Republicans leading the effort say the health care overhaul is the best case they can bring to a judge.

“We’re not trying to take every issue that we disagree with the president on,” said House Rules Committee Chairman Pete Sessions, who will lead the Wednesday hearing. “We’re going to pick that one that we believe has a lot of merit and widely recognized as an important issue.”

Proving that Obama misused his executive power is a long shot, most Republicans privately concede. Some even say that it is simply a way to quiet down the growing number of fringe Republicans who have said the party should move to impeach the president.

Obama and congressional Democrats are publicly dismissing talk of the lawsuit as little more than a desperate move by Republicans in the months before an election.

But senior GOP leadership aides describe a deliberate effort behind the scenes that they say gives them a fighting chance of defeating a sitting president in court.

“The wheels of justice may grind slowly, but they do grind and we are confident the court will decide in our favor against executive overreach,” a senior GOP leadership aide said.

For Boehner, incoming Majority Leader Kevin McCarthy (R-Calif.) and incoming Whip Steve Scalise (R-La.), the political downside of pursuing a lawsuit is minimal. Their rapport with the president is at an all-time low and going after Obama is never unpopular in the rightward-leaning House Republican Conference.

Republicans have already proved that they are unafraid to show an almost singular focus on undermining the law — they shut down the government over its funding last year. Despite their failure to defund the law and the unpopularity of the shutdown, the GOP is still poised to expand its majority in the November midterm elections.

Of course, Boehner could emerge with a splatter of egg on his face. If the House loses the suit, it will be his second consecutive defeat in court. The Supreme Court struck down the Defense of Marriage Act after Boehner spent millions of dollars defending it. The price tag for this suit is sure to be similar, but a senior GOP leadership aide said it’s “simply too soon to know” how much the Office of the House General Counsel will shell out. Top Republicans do concede that the legal proceedings will be lengthy.

But, this time, they say they have a winning strategy: Show that Congress has shown willingness to delay the employer mandate, but Obama went around Capitol Hill instead.

“The House has attempted to delay the employer mandate and instead of working with Congress, the president not only delayed Obamacare once, but twice; the second time creating his own legislative scheme for enforcement on categories of employers,” a Republican aide said. “These changes in law are beyond his constitutional authority and violated his duty to faithfully execute the law. By unilaterally making these changes, he has bypassed the constitutional requirement for amending statutory law — Congress legislates and the president executes.”

Unlike the DOMA case, which was authorized through the Bipartisan Legal Advisory Group — a panel made up of congressional leaders — Boehner is bringing a resolution to the floor in order to “eliminate any question about whether the litigation is authorized by the House,” the aide said.

Before this lawsuit even reaches a courtroom, it will occupy the attention of Capitol Hill in the few days remaining before the November election.

First, on Wednesday, the Rules Committee’s first hearing will feature testimony from Elizabeth Price Foley, a professor from Florida International University College of Law; Jonathan Turley, a professor of public interest law at The George Washington University; Simon Lazarus of the Constitutional Accountability Center; and Walter Dellinger, a partner at O’Melveny & Myers.

Next week, the committee will mark up the resolution, and then it will hit the House floor. The vote to authorize the suit will almost certainly be along party lines.

GOP lawmakers involved in Obamacare oversight say they see absolutely no downside.

“When people say is there a risk of doing this, of course there is. Anytime you go to court, by definition, one side wins and one side loses,” said Rep. Michael Burgess (R-Texas), a physician who is vice chairman of the Energy and Commerce subcommittee on health. “Is there a risk? Yes, of course there is a risk but the risk of inactivity, the risk of doing nothing, the risk of no action is that you can logically infer from this that anything passed by Congress can be changed by the president at any point that he feels it is inconvenient for him to go forward.”

The health subcommittee’s chairman, Rep. Joe Pitts, said even if the lawsuit fails, it shines light on Obama’s actions.

“He’s abused his power, and everyone is very, very aware now that he abused his executive authority by administrative actions, by executive orders,” the Pennsylvania Republican said.