A federal judge in Washington is set to hear arguments Wednesday on whether to reveal the identity of the foreign government-owned company that for months has challenged a grand jury subpoena issued as part of Special Counsel Robert Mueller's investigation into Russian interference in the 2016 presidential election.

The hearing before U.S. District Chief Judge Beryl Howell of the District of Columbia comes just days after the U.S. Supreme Court turned down the company's effort to resist Mueller's demand for information. The company, represented by a team from Alston & Bird, had argued it was protected by foreign sovereign immunity and that complying with the subpoena would violate the laws of its home country.

Since the Mueller investigation closed March 22, the special counsel's prosecution team has turned over the grand jury subpoena case to the U.S. Attorney's Office in Washington, a special counsel spokesman said.

The Reporters Committee for Freedom of the Press, represented by Gibson, Dunn & Crutcher partner Theodore Boutrous, has spearheaded the effort to pierce the secrecy of the case and make public documents that could reveal the foreign government-owned firm's identity and why Mueller's team sought information from the company.

The company, whose identity has remained secret through sealed court proceedings, has incurred a daily fine of $50,000 for its refusal to comply with the subpoena, amassing a sanction that appears to have exceeded more than $2 million.

The government hasn't said publicly whether it has made any attempt to enforce the civil penalty, and it's not clear whether the company has agreed now to cooperate with the Mueller grand jury.

With its appeal options exhausted, the company could enter negotiations with the Justice Department to comply with the grand jury subpoena—and perhaps gain the government's support for a fine reduction, according to lawyers who specialize in international law and white-collar enforcement.

“They've hit the end of the road in terms of judicial process,” said Cleary Gottlieb Steen & Hamilton partner Joon Kim, a former acting U.S. attorney in Manhattan. “There's no higher court. They don't have a lot of leverage now, and not a lot of other options left.”

To exert greater pressure, the Justice Department could try to seek a higher daily fine or ask for an order that the company's executives be arrested if they enter the United States, said Crowell & Moring partner Stuart Newberger.

“The solicitor general hasn't stopped working, the U.S. attorney's office hasn't stopped working. They have to decide first if they want to continue to investigate this company and then, if so, turn up the pressure now that the legal defense was rejected with finality,” said Newberger, a former assistant U.S. attorney in Washington and author of “The Forgotten Flight: Terrorism, Diplomacy and the Pursuit of Justice.” “There are other tools in the toolbox that prosecutors can bring—maybe assets in the country that can be frozen.”

Newberger, who is not involved in the Mueller case, said Howell holds some of the cards in the continued fight. “If the Department of Justice proceeds, Chief Judge Howell might ratchet up the pressure on the company and order that, when executives of the company come to the U.S., they could be arrested and put in prison for contempt,” he said. “All of these things are possibilities that the chief judge has the power to enforce. It's not over.”

There's no certainty the U.S. government will ever recover the $50,000 daily penalty that Howell imposed on the foreign-owned company. The amount wasn't the first time a foreign entity was hit with a steep sanction. In an unrelated case, U.S. District Judge Royce Lamberth in Washington fined Russia $50,000 daily in 2013 for its refusal to return sacred Jewish books to the United States. That case is still pending in the trial court.

In court Wednesday, Boutrous is expected to argue that the conclusion of Mueller's investigation last week should compel the public release of the foreign-owned company's identity. He has argued that the blanket sealing of the subpoena challenge was overbroad and ran against the First Amendment and “common law rights of access” to court proceedings.

Read the Gibson Dunn and Reporters Committee motion to unseal below: