WASHINGTON >> Angry at what they saw as the Obama administration’s frequent flouting of congressional authority, House Republicans last year began casting about for a way to fight back.

Jo-Marie St. Martin, counsel to Speaker John A. Boehner and a ferocious defender of the rights of the House, quietly put the word out that the leadership was looking for potential lawsuit targets so it could challenge the White House in court.

She and House lawyers combed through lists assembled by conservative lawmakers. They met with a private lawyer who had developed a legal theory about how best to counter the White House. The House counsel’s office analyzed various options, with charts listing the pros and cons.

They settled on the health care law, now at the center of a little-noticed legal fight that could redefine the balance of power in Washington. A federal judge is expected to rule soon on whether the House can sue the executive branch for usurping its authority over spending — its vaunted “power of the purse” — in a case resulting from years of bitter struggle between the Obama administration and the Republican House over who controls which levers of power.

“It was the perfect thing we had been looking for,” St. Martin said of the spending program started by the administration to help insurance companies offset new health coverage costs for consumers. “We were off and running.”

If Judge Rosemary M. Collyer of U.S. District Court lets the case proceed, it would break with a long history of the courts looking askance at such suits between the two branches and be the first time the House has won the right to sue the executive branch over appropriations power.

To an administration accustomed to opposition from congressional Republicans, the House suit is another partisan effort to unravel the health care law through the courts since Republicans have failed to do so in Congress despite scores of attempts. White House officials note that the administration successfully defended the Affordable Care Act at the Supreme Court twice and fared well in other legal skirmishes over executive authority.

“When you get these into court, the notion that the administration has been overreaching just doesn’t stand up,” said W. Neil Eggleston, the White House counsel. The Republicans’ lawsuit, he said, “is a case of them not being able do what they wanted through the constitutional process and then wanting to get the third branch involved.”

If the House prevails, it would be damaging, but not fatal, to the health care act, with nearly 6 million low-income consumers facing much higher deductibles, copays or other out-of-pocket costs unless the administration gets congressional approval for the insurance reimbursements, an unlikely occurrence. But the suit could backfire on Congress. Should the administration win, it could shift more decision-making on spending to the executive branch.

Despite criticism from congressional Democrats and some legal experts that he is turning a partisan political fight into a legal one, Boehner is resolute.

“This was clear as a bell to me that it needed to be done, and if we win this suit it will reverberate for decades,” he said in an interview. “This case goes to the constitutional structure of our government and to the heart of our democracy.”

Dating back to George Washington’s time, Congress and the White House have engaged in a tug of war over their respective powers. The strains have intensified as President Barack Obama, frustrated that Republicans have stalled his legislative priorities and blocked confirmation of some nominees, increasingly asserted executive power to accomplish his goals. (Obama poked fun at his reputation for acting unilaterally when he recently threatened to issue an executive order to keep Jon Stewart on “The Daily Show.”)

Scholars say the complaints of House Republicans that Obama is breaking new ground in presidential power grabs might be taken more seriously if they had not been so quiet when the administration of George W. Bush flexed its executive muscle on both foreign and domestic policy.

“What makes the current moment, if not historically unique, at least distinctive is the degree to which Congress’ vigilance over its constitutional authorities seems to vary according to partisan identification,” said Peter M. Shane, an Ohio State University professor who has written on executive power issues.

The current executive power fight began in early 2011 after Republicans took back the House and installed Boehner as speaker. To the shock of St. Martin, 55, a career Capitol Hill staff member, the Justice Department that February informed the new speaker that the Obama administration would no longer stand up for the Defense of Marriage Act, judging it to be unconstitutional. (The measure defines marriage as the union of a man and a woman.)

The House joined in defending the marriage law all the way to the Supreme Court, which ultimately overturned it. But that was just the first episode; the two sides clashed over environmental, immigration and Justice Department issues. After a Republican challenge, Obama was rebuked by the Supreme Court on appointing nominees while Congress was in recess.

St. Martin, little known beyond Capitol Hill but a major force with a broad portfolio within the speaker’s office, was in the middle of most of those fights. She met Boehner when he was a freshman troublemaker on the House Education and Labor Committee in the early 1990s and she was a young lawyer for committee Republicans. She offered him advice on how to use committee rules to aggravate majority Democrats, who were soon to fall from power under an assault from Republican agitators.

When Boehner lost his position as chairman of the House Republican Conference in a shake-up that followed election losses in 1998 and returned to the education committee, he and St. Martin reconnected. She has had his confidence and ear ever since.

After weighing what would constitute the best claim against the administration, the Republican legal staff settled on the health care law and the administration’s delaying of dates for requiring employers to provide health insurance. Setting dates is generally considered the domain of the legislature.

Then, a potentially more potent angle surfaced. Senior staff members on the Energy and Commerce Committee alerted St. Martin to a puzzling expenditure under the health law they discovered as they pored over budget documents in the Rayburn Office Building.

Though a request for $4 billion for insurance companies to cover cost sharing had been in Obama’s 2014 budget request, the staff experts were certain that Congress had never appropriated the money. In fact, the Senate had seemed to explicitly reject the appeal. Yet the money was flowing.

Excited Republicans seized on the spending as the perfect illustration of the Obama administration’s long reach into the exclusive domain of the legislative branch. If the House cannot lay claim to its spending power, its best weapon against executive excess, what could it ever sue over, Boehner and his legal team asked.

“Every child in this country is told as a mantra that the definitional power of Congress is the power of the purse,” said Jonathan Turley, the George Washington law professor representing the House in the case.

Lawyers for the administration, who were on the defensive in a combative May court hearing, say the decision to initially seek an appropriation for the insurance funding was a mistake. They say that officials later determined that the Department of Health and Human Services did not need any additional authority since the funding was a permanent program, akin to Social Security and Medicare.

And even if the money is being spent inappropriately, the administration argues that the House has no standing to sue because it is wrongly using the courts to pursue a political dispute. Such fights, Justice Department lawyers say, are more properly resolved by passing a corrective law, repealing the one at issue or applying leverage such as stalling other legislation or holding up nominations.

“There are any number of tools that the legislature can use to exert its influence on the executive branch,” Joel McElvain, the lead lawyer for the administration, told Collyer. “It does not need reference to the judiciary, which is why we’ve never seen a lawsuit like this one in the last 230 years.”

Even if they are set back at the district court level, administration officials say they believe they will eventually prevail. But House Republicans express confidence that they have made a persuasive case that the courts are the only option to halt an abuse of power and improper spending of nearly $136 billion over the next decade.

“The Obama administration, through magic, has created an entitlement program,” St. Martin said. “Everyone always argues you can fix every problem through the power of the purse. Well, I guess you can’t if they are just making it up.”

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