President Joe Biden blocked Nippon Steel’s nearly $15 billion deal to buy U.S. Steel on Friday. Nippon is a Japanese company, and the president said putting a large American steelmaker under foreign control would create risks for national security. But Nippon and U.S. Steel vehemently disagree, and they aren’t giving up.

The two steel firms are threatening to go to court to keep their deal alive. In a statement Friday, they said Biden’s decision left them “no choice” but to take all appropriate action to protect their legal rights. But it could be tough to prove the deal wouldn’t hurt national security, said Christine McDaniel, a senior research fellow at George Mason University’s Mercatus Center.

“If the U.S. government and the president firmly think that it will, it’s hard to see a court overturning that decision,” she said.

The steelmakers could appeal to the incoming administration. President-elect Donald Trump did say just last month that he’s against the deal. Still, McDaniel said, there might be a little wiggle room. A committee of cabinet members that evaluates foreign deals — the Committee on Foreign Investment in the United States — could decide to take a second look at it.

“Let’s say Trump comes in and he’s neutral, and the new people on CFIUS decide that it’s worth taking a second look at. They could continue the investigation, keep it open,” McDaniel said.

There’s a lot at stake here, of course for Nippon and U.S. Steel, but also for some powerful interests arrayed against them. Henrietta Treyz, co-founder of Veda Partners, an investment advisory firm, said there are real national security concerns.

“Concern about having a foreign ally — in this case Japan — own nonetheless a very critical part of U.S. infrastructure,” she said.

There’s another powerful voice against the deal: the United Steelworkers union. Nippon and U.S. Steel have promised to honor existing union contracts. But Sean Higgins of the Competitive Enterprise Institute, a free market think tank, said he understands why the union is wary.

“It would be difficult for them to negotiate with a foreign owner. It always is if you’re a U.S. union,” he said.

But Higgins added that the deal with Nippon could give U.S. Steel employees some job security by helping the company they work for grow and compete with China.