I would not be surprised to see the GOP deliberately decide to jettison the pro-Life vote once and for all. It would be insane, but I can see the writing just starting to be scratched on the wall.
What you suggest may happen has already happened -- 1976, Gerald Rudolph Ford, Jr., rejected prolife support. Many anti-abortion activists actually thought that GA Jimmy favored restrictions on abortion. He didn't: he misled those people.