Parties are a messy, messy business. I've left my last post up as an example of stillborn amatuer analysis. Political philosophy is not something I have had any decent training in, so even while the Democrat=positivist & Republican=capitalist associations might have a nugget of substance today, there is really no way to build off of them into a generalized theory of the two-party system. I love looking for, and occasionally finding real patterns, but in this case, patterns will only be yielded by a much more intensive historical study--which has probably already been done.
The significant thing, I think, is that in fact, it is better that parties actually be difficult to analyze. The less ideological a party is, the more difficult it will be to figure out. Appropriately, parties have always been a constellation of competing values of religion, philosophy, national interests, and international relations; the more that all of these values begin begin subsumed into a totalizing closed logical system, the easier my job is, yet the greater the opportunity for totalitarianism.
Positivism and capitalism are "hungry" systems; by their nature they have a gravitational pull on spheres of reality beyond their original intent. They become totalitarian when they become black holes of social thought, and eventually, of human lives. But in fact, the American historical landscape really has been a multi-way struggle between a complex mishmash of goals, and will continue to be such as long as Christianity continues to be an anti-ideological force, as well as other basically human dimensions of interests.