“The question going forward, of course, will be whether the Trump impeachment conditions the public to understand impeachment as a tool of normal politics, or whether it retains its exceptional character,” said Josh Chafetz, a constitutional law professor at Cornell Law School. “The Clinton impeachment does not seem to have been enough to make it a tool of normal politics, but maybe this time will be different.”

Top Democrats acknowledge being torn. Speaker Nancy Pelosi recalled recently that she was under pressure to initiate impeachment proceedings against Mr. Bush for invading Iraq on the false premise of weapons of mass destruction, but she resisted.

“I just didn’t want it to be a way of life in our country,” she said during a town hall on CNN.

Rahm Emanuel, who served in the Clinton White House during the impeachment, agrees that there is a risk that “we are going to normalize impeachment and it is going to have a cascading effect in the way Bork became a term,” he said, referring to Robert H. Bork, the Supreme Court nominee rejected after a fiery 1987 hearing that inflames conservatives to this day.