George Mason, a leading voice at the convention on the question of impeachment, said it was imperative for Congress to have the means to remove a president who had gained his office by undermining democracy and the rule of law.

“Shall the man who has practiced corruption, and by that means procured his appointment in the first instance, be suffered to escape punishment by repeating his guilt?” he asked.

Of course, bribery is not the same thing as depriving voters of information by paying hush money. But both interfere with the democratic process, said Laurence H. Tribe, a law professor at Harvard, the other author of “To End a Presidency” and a frequent critic of Mr. Trump.

“The felonies of which Cohen, in statements that were self-incriminating and thus particularly trustworthy, accused his former client, the president, didn’t literally involve bribery,” he said, referring to Michael D. Cohen, Mr. Trump’s former lawyer, “but certainly involved criminal conduct designed to reduce the risk that disclosure of his extramarital affairs and dalliances on the eve of the election would cost him the votes he ended up needing in places like Michigan, Pennsylvania and Wisconsin.”

Most scholars agree that the impeachment clause covers abuse of official power by a sitting president but not wholly private conduct committed before assuming office.

Earlier impeachment proceedings are instructive. When the House Judiciary Committee adopted articles of impeachment in 1974 against President Richard M. Nixon, it accused him of obstructing justice while in office by interfering with the F.B.I.’s investigation into the Watergate burglary. Mr. Nixon resigned rather than face what seemed like inevitable impeachment.

President Bill Clinton was impeached by the House in 1998 for obstruction of justice while in office in connection with a civil suit in a sexual harassment case and a grand jury investigation into his relationship with Monica Lewinsky, a White House intern. Legal experts have questioned whether the charges — which involved private rather than official conduct, some of it before Mr. Clinton became president, and no obvious abuse of presidential power — satisfied constitutional standards.