WASHINGTON — The idea was to talk about relief for farmers hurt by tariffs, with a couple of them standing behind him in cowboy hats. But it did not take long on Thursday for President Trump to go off on “Crazy Nancy” and “Crying Chuck” and “treason” and the effort to “take me down.”

The last time a president was threatened with impeachment, he made a point of not talking about it. This one cannot stop talking about it. Where Bill Clinton tried to appear above the mud fight, leaving it to aides and allies to wage the battle for him, Mr. Trump is determined to get down into the mud himself and wrestle with his enemies at every turn.

Some advisers worry that the president is giving oxygen to a fire that otherwise might burn out or at least be left to crackle in the background. Others agree with Mr. Trump that he has been treated so unfairly that he should take on his opponents frontally.

As for his critics, they have been left scratching their heads, wondering if Mr. Trump is actually trying to goad them into impeaching him on the theory that it would help him politically. Speaker Nancy Pelosi even told colleagues she thinks Mr. Trump “wants to be impeached.” He later denied it, saying, “I don’t think anybody wants to be impeached.” But not everyone was so sure.