WASHINGTON — (CNN) The Supreme Court isn’t the only federal court considering a challenge to the Affordable Care Act.

Just down the street from the high court, District Judge Rosemary M. Collyer in the District of Columbia is considering another challenge brought by House Republicans.

In the case, House Speaker John Boehner sets forth two claims: that the money for payments to insurance companies was not properly approved by Congress, and that the Obama administration attempted to rewrite sections of the landmark health care law concerning the employer mandate without permission from Congress.

“This suit concerns the continued viability of the separations of power doctrine,” Jonathan Turley, a George Washington University Law School professor who is representing the House, argued in court papers.

It’s an unusual case, and Collyer could decide in late June whether to allow the suit to go forward. That’s around the same time the Supreme Court will decide a separate challenge that could gut the law.

In short, June could be a crucial month for the future of the signature legislative achievement of the Obama administration.

But before getting to the merits of the claims, Turley has a high hurdle: he must prove to the court that the House has the legal right, or “standing,” to bring the case.

Lawyers for the Department of Justice have filed a motion to dismiss the lawsuit, which they refer to in court papers as “novel and unprecedented.” They also assert that the House lacks any concrete injury from the implementation of the law.

“The role that Congress played in enacting [a] statute does not give it, let alone on of its chambers, a ‘personal’ stake in the manner in which that statute is now implemented,” they wrote.

Last week, Collyer held a hearing on the standing issue and she seemed extremely skeptical — and, at times, hostile — to the DOJ’s position.

At one point she asked a Justice Department lawyer why the government seemed to assert that the case is just an “abstract disagreement” of the law. As the government kept trying to keep the case about the issue of standing and not about its legal merits, Collyer grew increasingly frustrated, and asked several questions regarding the appropriation to the insurance companies. At one point, she spoke about the “insult” to the House’s authority.

On Monday, Collyer asked for more information about the appropriations, signaling the possibility that she may not think the case should be dismissed.

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