Republican politicians do not just have to think about the will of the voter. They have to think about the will of the Republican base, because voter appeal won't matter if they don't get on the ballot at all. The republican base is not representative of the population in general, and they are always assessing if candidates are sufficiently devout.
Yes, it's true the Republicans have to think about the will of their base. The really unfortunate fact is that the rightist base has proven to be rather biddable, they'll believe whatever they're told as long as the one doing the telling is a well-known Conservative Icon. Think right-wing talk radio hosts, religious leaders, rising-star politicians, etc. and the websites and online communities that support them. From these sources the Conventional Wisdom of modern American Conservatism is distilled and dispersed to the Red State faithful, who are happy to lap it up. Such Conventional Wisdom is never questioned, alas. So if you're a strategist for the Republican party, all you really need to do is buy yourself an established Icon or two to "fire up" the base, in whatever manner you wish to, and... Ta-da! It's done, they'll believe what you want them to, regardless of any contradictory evidence.
It's not a pretty picture, but that's how it works. Science or reality never even enter the picture. It's the only explanation for why these people still believe in things like tax cuts for the rich stimulating the economy and creating jobs. I mean, they've had something like 20 years to see EXACTLY how ineffective such policies truly are, but Conventional Wisdom still says they work, so expect all the Republican candidates to include them in their platforms. It's pathetic.