House Republicans' lawsuit against the Obama administration might have gotten an unexpected boost this week from the Supreme Court.

In a new legal filing Tuesday, attorneys for the House GOP said there's a fresh precedent supporting their suit challenging the administration's implementation of Obamacare—the Supreme Court's ruling Monday on congressional redistricting.

Although the two issues aren't directly related, the House's lawyers said the high court's decision could help Republicans overcome their biggest hurdle: establishing that the House has standing to sue the executive branch.

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House Republicans are arguing that the Obama administration injured the House, as an institution, by funding a particular part of Obamacare even though Congress did not appropriate money to fund that program. Their biggest challenge, legal experts say, will likely be to convince the courts that the House has a legal right to sue, and that this isn't simply a political dispute.

But the Supreme Court upheld a somewhat similar view of institutional standing in its redistricting decision this week. In Arizona, voters chose to give an independent panel the power to draw new congressional districts—power that used to rest with the state legislature. The state legislature sued, alleging that the referendum stripped lawmakers of their constitutional authority.

They lost, as the Court said the independent redistricting panel was fine. But it also said the state legislature had the standing to bring the lawsuit. And that, House Republicans argue, means their challenge to the Obama administration should also be able to proceed.

"The Court rejected defendants' arguments—and the arguments of the Administration as amicus—that the State Legislature suffered no cognizable injury and that any institutional claim of injury was too 'speculative,' 'premature,' 'hypothetical,' and 'conjectural' to confer standing," Jonathan Turley, the attorney representing the House, said in Tuesday's court filing. 

But Obamacare supporters say the Arizona redistricting decision isn't actually that powerful. They point to a footnote in which the Supreme Court explicitly said its decision about the Arizona legislature's standing had no bearing on federal disputes.

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"The case before us does not touch or concern the question whether Congress has standing to bring a suit against the President. There is no federal analogue to Arizona's initiative power, and a suit between Congress and the President would raise separation-of-powers concerns absent here," the Supreme Court's 5-4 decision says.

Timothy Jost, a law professor at Washington & Lee University and a strong supporter of the health care law, said that's enough to keep the two lawsuits separate.

"I would think the footnote is directly aimed at the House v. Burwell situation," he said. 

House Republicans are challenging the way the Obama administration implemented one of the Affordable Care Act's subsidies. The law offers financial assistance, paid directly to insurance companies, to help low-income families lower their co-pays and other out-of-pocket costs.

Republicans say the law was written to require that Congress set aside funding specifically for the cost-sharing subsidies, but that the administration has been handing out the payments even though Congress never actually appropriated the money for them.

The cost-sharing subsidies at issue in the House's lawsuit are separate from the premium subsidies the Supreme Court upheld last week in King v. Burwell. Because the two programs are authorized separately, and funded through different means, the administration's victory in the King case shouldn't affect the House's challenge, Republicans argue.

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"This changes nothing with regard to the lawsuit that we filed against the administration over their source of payments to insurers," House Speaker John Boehner told reporters last week. "They're paying insurers out of an account that's never been appropriated, and they've taken money from elsewhere in the law to do that. I think it violates the Constitution. It certainly violates Congress' prerogative to appropriate funds."

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