“Under the circumstances of the current so-called impeachment inquiry, it would constitute an unprecedented privatization of impeachment,” Mr. Collins said of Mr. Berke’s participation. He added, “If it’s win at all costs, Mr. Chairman, then we have a problem.”

Hand aloft, in a “Cool it” gesture

3. Representative Zoe Lofgren, Democrat of California

Ms. Lofgren is a crucial member of the committee’s brain trust. She served as a Democratic staff member for the panel during the impeachment investigation of President Richard M. Nixon and was a member herself when the committee voted to recommend impeaching President Bill Clinton.

This time, though, she has made no secret of her reservations about Democrats’ case and the wisdom of pursuing an impeachment strictly along partisan lines.

She also serves as the head of the House Administration Committee, and, as such, is stepping in as something of an arbiter to this rules dispute. As far as her committee is concerned, she said, it is well within the rules for Mr. Berke to ask questions.

at mr. nadler’s right hand

4. Barry H. Berke, a Democratic lawyer for the committee

Mr. Berke is the subject of the particular fight playing out here. A partner at the New York firm Kramer Levin with strong connections to Democrats (he once represented Mayor Bill de Blasio of New York in a federal investigation into the mayor’s campaign fund-raising), Mr. Berke was hired by Mr. Nadler last winter to help the committee shape its investigative work. . Up until Tuesday, he had labored mostly behind the scenes. The stage was set for him to take a more prominent role last week when the committee approved new procedures governing its impeachment investigation including allowing for staff lawyers to question witnesses directly after lawmakers have had their turns.

Mr. Berke’s rapid-fire cross-examination of Mr. Lewandowski, when it finally commenced, drew widespread praise and highlighted just how choppy and unproductive the typical questioning by lawmakers in hearings like these can be. Most notably, Mr. Berke was able to force the hearing’s sharp-tongued witness to admit he had been less than truthful about his involvement with the special counsel in national television interviews.

“I have no obligation not to be dishonest to the media because they are as dishonest as anybody else,” Mr. Lewandowski said.