“He is basically thumbing his nose at the Congress itself, saying I don’t recognize you,” Mr. Cohen, who heads an international consulting and lobbying firm, said in an interview. “I am surprised there aren’t more defenders of the Constitution. They are there to be a check on abuse of power. If they are willing to submit that to the executive, then they have no business being in office.”

Republican opposition in both the House and the Senate to pushing ahead with such inquiries is crucial because, as history has shown with the Watergate and Iran-contra scandals, such investigations can gain legitimacy only when members of the president’s own party support them. Intense partisanship surrounded those investigations as well, but with Republican lawmakers like Mr. Cohen and a handful of others showing some willingness to aggressively question the administration, the White House was forced to be more accountable and cooperative.

One important question today is whether there are any William Cohens or Larry Hogans, a Maryland Republican who was a surprising early backer of Nixon’s impeachment, willing to support more investigation or if Republicans will remain essentially united behind the president.

That’s a question that Representative Zoe Lofgren, Democrat of California and a long-serving Judiciary Committee member who was on the panel’s staff in the 1970s, has been asking.

“At this point, where is our Caldwell Butler? Where’s our Bill Cohen? Where’s our Hamilton Fish? Where’s our Tom Railsback?” Ms. Lofgren said in a recent interview as she listed Republican members of the Judiciary Committee who voted in 1974 to impeach Nixon. “I don’t see that on the Judiciary Committee or in the House. And because I want to believe that every member of Congress who took an oath to protect and defend the Constitution meant it, having further oversight of these matters is worth doing.”