In a scheduling order issued following Thursday's hearing, Judge Chutkan said she would allow special counsel Jack Smith to file a comprehensive brief on presidential immunity by Sept. 26.

Chutkan's order allows Smith and his prosecutors to essentially defend their superseding indictment by presenting grand jury testimony and evidence that they believe bolsters their argument -- something that Trump's lawyers adamantly opposed during Thursday's hearing, because it departs from normal federal court procedure regarding which side gets to file papers first.

Trump's lawyers also suggested that such a filing would allow the special counsel to cherry-pick evidence.

As expected, the order contains no trial date for the case, as Chutkan acknowledged in court Thursday that setting such a date -- given the approaching November election -- would be "an exercise in futility."

After arguments concluded, Judge Chutkan adjourned the hearing.

She said she would issue a scheduling order as soon as possible regarding the next steps in the case.

Special counsel Jack Smith, who was present during the hearing, departed with multiple members of his team.

Judge Chutkan says she is inclined to let both sides file more motions or briefs related to the Trump's teams challenges to the case on statutory grounds -- but she also made clear that she believes those statutory issues can be handled at the same time that the parties also try to resolve immunity-related issues.

“Immunity is the lynchpin here,” and both sets of issues can be handled concurrently, she said.

Prosecutor Tom Windom made some final points supporting the prosecution's views. Among them, he noted that in the New York hush money case against Trump, Trump's legal team filed a 52-page motion to vacate the case only nine days after the SCOTUS ruling related to immunity.

"The defense can move comprehensively, quickly and well, and so can we," and the judge should consider that in setting the schedule in this case, Windom said.

Defense attorney John Lauro then said he wanted to speak briefly. Chutkan said it had to be brief, saying, "I don't need any more rhetoric on how serious and grave this is."

"It's not rhetoric, it's called legal argument," Lauro shot back.

Lauro again insisted that special counsel Jack Smith's appointment was unlawful. "We have an illegitimate prosecutor. We have an illegitimate indictment," he said.