There are two very important subtexts to this.
First - Americans are sick to the point of exhaustion of divisiveness in politics. Sure, the average American doesn't pay close attention, but they do get a sense of the constant bickering and entrenched attitudes. Pressing impeachment is simply putting a banner and a neon sign over the Republicans to advertise themselves as the party of division. Impeachment will make a statement alright, and the public will respond accordingly.
Second - This addresses why so many want impeachment, when you elect a Republican, what do you get? I honestly don't know, my political barometer, my moderate friend, has no clue. Right now, the only thing Republicans seem to be is not Democrats, (in title, not in fact). Republicans don't have to be hardcore conservatives down the line. But they do need to say what they mean, and mean what they say. Be something, not just run as "not one of them".