Pretty insightful post.  You know, I always find it interesting to watch Fox News because there's so much conservative editorializing that it allows the commentators, such as O'Reilly, to start to plunge into some really sophisticated and nuanced discourse about conservatism, and this magnifying glass is a good way to discern splits within the Republican coalition.

The truth is, though, the situation is even worse than you suggest for the Republican coalition.  That's because there's at least a 3-way division in the Party, in fact.  There are...

1.  The religious, traditional family, blue-collar populist types.  Socially conservative and financially more corporativist (you could say they are more financially "liberal," but not in the classical sense, only in the strange American sense of "liberalism").  This group has been relatively disappointed and demoralized during Bush's 2nd term, mainly because Bush promised a bunch of attention to the demands of this part of the base during the election campaigns, but this was pretty much a cynical ploy for support, as far as I can tell (just as the fake Texas accent from Kennebunkport Yalie boy George is).  The people who have real power in the Bush administration aren't going to get caught up in any volatile social reforms and silly Crusade for Christ notions.  The real people with power are...

2.  Neoconservatives.  Geopolitical masterminds who are not afraid to ring up massive debts and use socialism for the rich to support military spending (the Pentagon subsidy system for the military industrial complex, etc.), plus they are imperial hardliners.  Their primary goal is to expand U.S. geopolitical and military strength in the world.   They don't have much of a popular base of support, which is why they have to dedicate some of their rhetoric to humoring the aforementioned religious populist fantasies, as well as try to placate the...

3.  Neoliberals.  Socially liberal and economically conservative.  Includes yuppies, the Neil Boortz "fair-tax" types, and economic free-market capitalist zealots who generally place a higher priority on "fiscal responsibility" (denouncing welfare, "handouts," entitlement spending, etc.)   These are usually at most imperial realists who think that the U.S. should rely more on economic and diplomatic devices (WTO, IMF, UN) rather than military devices for spreading U.S. hegemony around the globe.  This category also includes the Ron Paul supporter types who want to drastically cut military commitments and spending and who want to restore some civil liberties.

So group 1 gets condescendingly ignored by group 2 and opposed by group 3 on a number of issues.   Group 2 feels fettered, distracted, and annoyed by the priorities of groups 1 and 3. And group 3 has reasons to oppose many of the policies of group 1, and group 2 when the military adventures aren't going well and start to drag on and become an economic liability.

The Republican Party is at a world-historical juncture right now.  It is in serious trouble.  20 years from now, it may no longer exist.  

In short, I guess, the thing that most strongly unites Republicans is fear of the other side.  Now, what is the base of this other side?  I would summarize it as:

Beneficiaries of the New Deal economic legacy + children of the '60s.  So you've got your labor unions, working class urban citizens, + civil rights, women's rights, gay rights, all the progressive equal-opportunity identity politics stuff, as well as the anti-war and environmentalist stuff that got started in the '60s. That's actually a pretty congruent base.  No internal conflicts of interest. 

What I don't understand is, for some reason the Democrat leaders always seem to have a problem with being loyal to this base.  Shave off a little of the New Deal here and there, support this or that war, be lukewarm on gay marriage, etc.  Either they seem to think that this base is not numerically large enough to carry them forward single-handedly, or they have another base that they need to honor...corporate lobbyists, for instance.  Inevitably a chunk of the base gets demoralized, doesn't show up to vote for votes for Ralph Nader, and are the Democrats any better off in the end? 

(By the way, yes, I am implying that it is equally the Democrats' fault, just as much as it is Ralph Nader's, if the Democrats lose votes to Ralph Nader again this election.  This is entirely preventable, if only the Democrats are willing to be more liberal.  (But then, of course, they'd have to give up on some centrist voters.  But sorry, there's only so much of a width of the political spectrum that you can straddle simultaneously, and if the population doesn't happen to be densely concentrated in any region of the spectrum that you might be able to settle on, then tough luck...you're just not going to win any elections until there is a significant shift in grassroots attitudes towards your end of the spectrum.))

I agree with absolutely everything Matthew just wrote. (I'd add, also, that we shouldn't worry about losing "centrist voters" because, as I've argued before, they don't exist. A move to the left is completely sound political strategy. Democrats' continuing ties to establishment/centrist politics probably have more to do with both ideological Harvard-ism and of course the importance of Wall Street fundraising.)