But that would suggest its problem doesn't come from being the party of capital that fakes that it isn't, but rather that the capital it represents is itself politically incoherent."
[WS:] I agree with your point that "being a party of capital" - or more generally alleging that political parties are merely shadows of commercial interests - is not very useful in explaining the actual behavior. However, I also think that you introduce that explanation through aback door when you claim divisions withing the capitalist class as a reason.
I'd argue that political party system in the US plays a significant role in creating or maintaining those divisions - much more so than the political party/governance system in most other developed countries. Political parties in the US are much more deeply engaged in political patronage of special interest groups, and thus play a more active role in maintaining a system of governance that is conducive to patronage than their counterparts in other developed countries. This point has been raised by several political scientists (Schattschneider, Evans, Skocpol, Lijphart) but remains rather obscure.
Case in point - Obama's health care reform. The design for the reform was essentially crafted by Republicans. So if ideology was the main consideration, one would expect that Republicans to sit quietly and smirk when Obama was doing the dirty work for them. However, is dispensation of patronage was the main concern, "stealing" someone's "turf" by by appropriating their agenda would be a grave offense calling for revenge (just as it is in gang turf wars.) And this is precisely what actually happened.
In sum, the lack of coherence of the capitalist class in the US that you claim is, for a large part, an effect of the US political party system and its patronage dispensation, which is quite "unique" in the developed world (although not so in the developing one.)
Wojtek