I wonder if the stubborn belief that impeaching Trump will make him more popular somehow has its origin in the right's denial about just how popular Clinton was during his presidency. Clinton was really popular, and yet the right consistently portrayed him to be a beleaguered President. So rather than acknowledge that Clinton was actually well liked when he was in office, the right has come up with this theory that Clinton's numbers are inflated because he benefited from Newt Gingrich's overreach on impeachment.no one has been able to explain the mechanism by which impeaching the unpopular, widely-disliked president makes him *more popular*— b-boy bouiebaisse (@jbouie) September 27, 2019
While it is true that Clinton's ratings did seem to get a bounce when the Republicans began their impeachment effort, he was already pretty popular before that effort began. (I think a much more plausible argument for Clinton's high approval ratings is the dot-com bubble. You know, because it was the economy, stupid)
So the post-hoc argument doesn't really hold up. but even if the secret to Clinton's popularity was impeachment turned out to be true, it doesn't follow that the same thing will happen when Trump is impeached. Clinton's popularity went up when the Republicans impeached him because he was already popular. The lesson of the Clinton impeachment is impeaching a popular President is not popular, and tends to make the popular President even more popular.
Trump, on the other hand, is really unpopular and he has remained consistently unpopular throughout his term. In fact, Trump is the only President since the beginning of modern polling whose approval rating has never exceeded his disapproval rating. That's an unprecedented level of unpopularity that has remained resilient for almost three years. In fact, it seems that Trump has a hard ceiling of support of around 45% and 52% of Americans say they "definitely won't" vote for Trump next year. Even if a majority is never on board with impeachment, the guy is too broadly disliked for him to get any sympathy bounce.