“Haven’t we just been through a lot with the Clintons?” Mr. Trump asked. “The work of government would grind to a halt if she were ever elected.”

The tactic is a rejection of the nation’s need of a functioning government and a tacit concession that Mr. Trump may be losing and that he can be saved only by more scare tactics. Other Republican candidates in tight races have picked up this theme. The G.O.P. phrase du jour is “constitutional crisis,” depicting a hog-tied executive and a Republican Congress obsessed with perpetuating their demonization of Mrs. Clinton. Senator Richard Burr, campaigning for re-election in North Carolina, took the Trump fantasy one step further, telling supporters: “Could she pardon herself? And the answer is yes.”

Rudy Giuliani, one of Mr. Trump’s most zealous acolytes, echoed this cry to carry the battle forward into a Clinton administration. “I guarantee you in one year she’ll be impeached and indicted,” Mr. Giuliani promised Iowa voters this week. “It’s just going to happen. We’re going to sort of vote for a Watergate.”

As nonsensical as this strategy appears, these threats could cause real damage by encouraging Republicans in the next Congress to effectively take the government hostage, exacting revenge by making sure that nothing Mrs. Clinton proposes ever comes to pass. President Obama put it well in underlining the dangers. “Right now, because a lot of them think that Trump will lose, they’re already promising even more unprecedented dysfunction in Washington,” he told North Carolina voters this week. “How does our democracy function like that?”

That is not a question remotely of interest to Mr. Trump, in his kamikaze politicking. Yet in recalling the tumultuous impeachment of President Bill Clinton, Mr. Trump neglects to note that he was opposed to it, writing in 2000 that he “got a chuckle out of all the moralists in Congress and in the media.” Mr. Giuliani, before his servile devotion to Mr. Trump, also opposed Mr. Clinton’s impeachment.