Tuesday’s request from House counsel Doug Letter indicates they’ll take Jackson up on her offer.

“Given that the House’s impeachment inquiry is proceeding rapidly, the Committee has a finite window of time to effectively obtain and consider McGahn’s testimony,” Letter wrote in a five-page request.

That window is indeed shrinking, with the House Intelligence Committee stacking up witnesses over the last two weeks in a series of rapid-fire public hearings.

Letter explained that the House Judiciary Committee planned to have its own impeachment hearings after the conclusion of Intelligence Committee’s efforts “and would aim to obtain Mr. McGahn’s testimony at that time.”

“Thus, there is an urgent need for final resolution of the matter now pending before this Court,” Letter added.

The Justice Department has tried to block McGahn’s testimony, arguing that the ex-Trump aide who appeared hundreds of times in Mueller’s final report can essentially ignore a congressional subpoena related to his time in the White House. During arguments before Jackson, department lawyers said the federal courts shouldn’t weigh in on a dispute between Congress and the executive branch.

House Democrats started seeking McGahn’s testimony in early 2019, including him among the more than 80 people and organizations in the president’s orbit who got letters demanding documents from the Judiciary Committee in March. Democrats issued a subpoena for materials from McGahn covering 30 different topics after the Mueller report went public in April describing numerous instances where Trump tried to stymie or outright end the Russia investigation.

McGahn skipped a public hearing called for him in May, and Democrats followed up with a lawsuit in August.

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In their request on Tuesday, Democrats said their “need for McGahn’s testimony has become even more pressing” since then, after House Speaker Nancy Pelosi endorsed impeachment proceedings that pivot off Trump’s attempts to pressure Ukraine into investigating his political opponents.

A source familiar with McGahn’s thinking said the former White House counsel’s testimony would depend on whether any decision from Jackson got stayed pending an appeal. “If it isn’t, he will comply. If it is stayed, he will await the decision of the higher court,” the source said.

Letter explained to Jackson that Democrats investigating impeachment were also pressing a federal appeals court for a speedy decision as it weighs the validity of a lower-court ruling that would give them the rights to see Mueller’s most sensitive grand jury materials.

In that case, Letter told the U.S. Court of Appeals for the D.C. Circuit during oral arguments on Monday that it needed access to the Mueller documents to determine whether the president lied or gave misleading written answers to the special counsel.