"When voters are given a choice between voting for a Republican, or a Democrat who acts like a Republican, they'll vote for the Republican every time."

Ain't necessarily so. Tony Blair managed to get not only elected but reelected as a Labour (cf Democrat) politician advocating Conservative (cf Republican) policies.

Now the Conservatives reckon that their only way back to power is to posture as saviours of the public services that they themselves wrecked, which is as close as you can get to a reversal of polarity by both parties.