The study of public opinion has been a sixty-plus year long search for what we call constraint – the degree to which a belief held by an individual is predictive of other beliefs. A constrained belief system is an internally consistent one; for example, if you believe in lower taxes we would expect you to believe in lower spending as well. This seems like a remarkably obvious concept, but since Converse we've found that frighteningly few Americans organize or constrain their beliefs about politics into anything approaching a coherent worldview. This is why so many voters hold ideas that make absolutely no sense together, even when the conflicts are glaring.
The modern Republican ideology is often criticized for inconsistency on the grounds that it abhors Big Government but promotes government involvement in our private lives through social issues. It is strongly pro individual rights in theory but with dozens of "exceptions" in practice. That said, I see a kind of constraint across prominent political issues in the contemporary GOP: they generally believe that problems have supply side solutions. Poverty exists because the welfare state enables it; without food stamps and TANF, people would be working. Illegal immigration is solved with guns and border fences, not by eliminating the demand (American employers who knowingly employ immigrants of dubious legality). You get the picture.
There are, however, two glaring exceptions to the supply-as-constraint idea. First, the drug war is very much a demand side problem to Republicans. Sure, some efforts are made to stop the importation of drugs at the border, but the vast majority of law enforcement resources (including manpower and time) in the War on Drugs is devoted to rounding up users and small-time dealers (who are merely the retail kiosk of a system that generates supply much farther up the food chain). Second, gun violence is emphatically a demand-side problem. The supply and availability of guns certainly isn't seen as a problem. The problem is what some individuals ("Bad Apples", of course) decide to do with the plethora of firepower to be had.
I'm sure there are other examples of issues that Republicans define as supply problems as well as others that are considered demand problems. I find it interesting and somewhat revealing that two prominent issues that contradict the overarching supply side understanding of socioeconomic and political issues are the War on Drugs – when seen as a demand problem, the state responds by putting countless poor and/or dark-skinned people in prison – and gun politics as a whole, where a demand-based explanation ensures widespread access to the guns people need to make themselves feel secure and/or powerful.
So I'd argue that the average Gingrich / Perry voter does have a constrained set of political beliefs. The problem is that their underlying motivations – dislike of the poor/dark and gun fetishism – are stronger than any ideology or worldview that might attempt to constrain them.