A federal judge in District of Columbia repeatedly evinced exasperation with the U.S. Justice Department's arguments that former White House counsel Don McGahn can't comply with a subpoena for his testimony as part of the House's impeachment inquiry, questioning when the federal government believed former officials could speak about their experiences working for the executive branch.

U.S. District Judge Ketanji Brown Jackson of the District of Columbia on Thursday trained her focus on Justice Department deputy assistant attorney James Burnham's arguments that the House could not go to court to enforce the subpoena, and that neither current or former top White House aides could be made to testify before Congress.

The House Judiciary Committee filed its lawsuit over McGahn's testimony earlier this year, and at the time characterized the need for the former White House counsel to publicly speak about potential obstruction of justice by as key to the panel's decision on "whether to recommend articles of impeachment against the President."

McGahn has refused to comply with a subpoena for his testimony at the direction of the White House.

For two hours, Jackson solely heard arguments about whether or not the court could intervene in the case. She signaled throughout that she believed it was proper for the House to go to court to enforce a subpoena.

At times, Jackson's voice rose and seemed to express frustration as she took issue with the claim that McGahn couldn't be sued in his capacity as a former executive branch official because of the protections offered to those in the branch.

She pointed out that former officials regularly speak publicly about their prior experiences working in the White House or other agencies, including during media appearances. 

"The House is suing Mr. McGahn in his capacity as a former executive branch official," Jackson said. "Doesn't that sweep so broadly that, for the rest of Mr. McGahn's life, anyone who wants to ask him about his role as a former executive branch official" would be impacted by those same privilege issues.

And she pushed DOJ on why the House can't go to court to enforce a subpoena, the way private parties often do during typical court proceedings.

"So what does checks and balances mean?" Jackson asked at one point. "How can the legislative actually exercise oversight with respect to the executive, unless it has some ability to enforce its inquiries" on information?

And later she asked Burnham if DOJ's position is that "there is no circumstance under which the House" could ever come to court.

"As a general proposition, I think that's correct," Burnham said.

U.S. House of Representatives Associate General Counsel Megan Barbero argued that the House had the right to access the information McGahn has to offer about the potential acts of obstruction of justice as laid out in the Mueller report.

Jackson asked Barbero about DOJ's argument that there is enough information in the Mueller report to inform the committee's actions. Barbero said lawmakers need a chance to ask McGahn follow-up questions and cross-examine him as a witness.

"The president has disputed Mr. McGahn's account and has discredited him," Barbero said, which means the House needs to question the former White House lawyer further.

Later in the hearing, Burnham argued that the case centers on a dispute between the House and the executive branch because the right to assert absolute immunity laid with the president.

He said that meant privilege issues still applied to McGahn, even though the attorney has left the White House.

"It seems odd to me that it survives your existence" at the White House, Jackson said at one point, sounded frustrated.

Burnham at one point seemed to acknowledge that he could be facing an uphill battle in Jackson's court.

"If you don't think the president has absolute immunity, that's going to be a serious problem for my argument," he said at one point.

"I don't know if that's the case," Jackson replied, adding that she was trying to further understand the Justice Department's argument.

House general counsel Douglas Letter said the arguments the White House could generally deploy in saying McGahn can't testify, like it impacting his ability to do his job, don't apply because McGahn is now a private citizen.

"He's in private practice of law, earning a profit," Letter said of McGahn, now a partner at Jones Day. "Obviously he can take some time to respond to subpoenas issued by the House."

When Letter referenced the House's impeachment inquiry as further reason that McGahn needs to testify, Brown asked how that applies to this case, as the inquiry wasn't formally announced until after this lawsuit was filed.

Letter said the Judiciary Committee was considering impeachment at the time the complaint was filed. And he pointed to the Office of Legal Counsel opinion against the indictment of a sitting president as backing his argument.

"How can the Trump administration, on the one hand, say you can't criminally prosecute" a sitting president, Letter said, "but when you try to come up with the evidence to see whether you can impeach him or not, we're going to stonewall you."