If they did this, they would make pro-choice Democrats look like extremists. Unfortunately, they instead let themselves be painted as people who would willingly see women raped and then forced to birth and raise the rapists' children (I'm not saying the Republicans really are like that, but that they get painted that way).
What Republicans need to publically acknowledge is that not everything that is wrong and abhorrent can be outlawed, and that it would be both foolish and ineffective to push for restrictions that the majority of people wouldn't support, unless or until such time as the majority of people support them. While most Republicans are well aware that there's no possibility of suddenly passing a complete ban on abortion which extends all the way to cover certain contraceptives, there are a significant number of people who vote Democrat out of fear that the Republicans would do precisely that.
There's the problem. Actually, I've become convinced that the Republican heirarchy is nearly as leftist as the Demonrats. They've never lost an election by running to the right, but they keep going for "the big tent", ie; running off the people who do vote for them in order to get the votes of people who don't like them. I've ceased to believe that they're stupid enough to believe that conservatism doesn't win elections.