The sad truth is that the majority of GOP voters, who are mostly White poor working class folk, do not want a free market where no one gets handouts, because, after all, they're poor, and all poor people want handouts.
The only different between the lower-middle class GOP voter and a cafe liberal is that the former doesn't like to admit that he wants a handout. Saying he likes a welfare-free government makes him feel proud, but when he gets to the polls, ultimately, his pocketbook will do the talking.
Then the natural questions is: well, if these working-class GOP voters desperately want handouts, why do they keep voting the party that claims to want to deny handouts to the poor?
The reason is that these working-class GOP folk believe that the Dems will take some of the handouts that are supposed to belong to White people like them and give it to Latinos, Blacks, gays, etc. In other words, their fear is that they will lose welfare benefits to people of color.
So, in a nutshell, the right wing--which consists predominantly of uneducated, working class people, is almost just as much for welfare for the poor as the cafe liberals in the Democratic Party. They just want all the welfare checks for them, i. e. White people, as opposed to "minorities."