I think the "we don't like what you've done" mechanism is a recall election rather than an impeachment. Of course, lots of places don't even have those.

Under this same logic the Patient Protection and Affordable Care Act (aka Obamacare) would have lead to the impeachment of the President and most of the Democrats in Congress. It was HUGELY unpopular and has only recently become so-so... 5 YEARS after it was passed.