I think you are half right.
I am not sure if the Republican politicians believe that nonsense, they simply believe it would resonate with their voters.
I saw this over and over during the run-up to the elections: Republicans were not articulating a platform for their voters. The first thing out of their mouths was, we need to save ourselves from failed policies, and then they rattle off a few generalizations (i.e. failed economic policies, crime out of control in our streets, etc. etc etc.). They seemed to think that all they had to do was demonize the other side. Frankly, it made the candidates look more opportunistic (want to jump on the bandwagon of anti-left causes) than intelligent leaders that could come up with a plan to manage their districts.
Frankly, their deadfast conviction to the popular notion of a red wave was their undoing. I think the election showed that voters care passionately about issues, and issues that effect them on a local level. The right to an abortion is one of those.