I mean the logic is that republican voters are willing to vote against the economic interests of pretty much everyone to fulfill some fanatical ideology that only a minority of the population actually holds. That seems crazy to me, but I don't know if I consider myself an average American though. EDIT: Also, when I say minority I'm not sure how much of a minority it actually is anymore. The domination of religious teaching in politics has been so volatile in U.S. politics that calling it a minority is wrong actually.
The goal isn't "average americans" the goal is those poor old ladies and gentlemen in the nursing homes who have been disenfranchised and whose children don't visit them enough but maybe we can talk them into coming down to the American Legion hall to preserve a future where Adam and Steve can't get married for little Timmy and Tammy, even if they're ungrateful little wretches. Seriously. Republican demographics skew so old it hurts. That's probably why they're pushing so hard into Marco Rubio, he's the only one with a prayer of attracting voters under 60. I'd even go as far as to say Marco Rubio would be a Democrat if he weren't clever enough to seize an opening.
The reason they target them is because it is the most effective group to target with their toxic legislation. If you think about it that class of people are usually a few generations behind in terms of technology so they can't really keep a close eye on politics. In most cases the republican party can mask their economic policy behind paper thin social "reform" because lets be honest none of them will be around to feel the impact of those economic policies. To add to all of that they are literally the most politically active class in the U.S.(They vote on literally everything). It makes absolute sense that the republicans would target them. It will be interesting to see how the Republican party reform to get ahold of a younger vote.