The big picture: The lawsuit follows a court filing last month seeking the release of grand jury materials from the Mueller report in which Nadler wrote that the committee had already begun "investigating whether to recommend articles of impeachment." He has declined, however, to label the investigation a formal "impeachment inquiry."

Nadler said on MSNBC this week that court decisions in these two key lawsuits will probably be reached by the end of October, and that the committee will have hearings with "witnesses who are not dependent on the court proceedings" in September and October."

Under this timeline, Nadler said that a decision on whether to report articles of impeachment would likely come "late in the fall, in the latter part of the year."

Between the lines: Nadler told Politico in June that the McGahn court case is "key to everything" because it addresses the question of whether the White House can assert "absolute immunity" over witnesses. "It’s one thing to tell a judge blanket immunity is not a right thing," Nadler said. "It’s another thing when a judge can see what that means in actuality, and how absurd it is."

Nadler added that former White House communications director Hope Hicks will talk to congressional investigators "only under legal compulsion." Hicks sat for a closed-door interview with the committee in June, but was blocked by White House lawyers from answering any questions about her time in the administration.

The other side ... McGahn's lawyer said in a statement:

"People should not forget that Don McGahn is a lawyer and has an ethical obligation to protect client confidences, and as I have said before, Don does not believe he witnessed any violation of law. And the President instructed Don to cooperate fully with the Special Counsel but directed him not to testify to Congress unless the White House and the Committee reached an accommodation. When faced with competing demands from co-equal branches of government, Don will follow his former client’s instruction, absent a contrary decision from the federal judiciary."

Read the lawsuit:

Go deeper: The impeachment slow-drip