...and largely something that both "sides" (the 3/4 of the country who find the Tea Partiers insane and ignorant and the Insane, Ignorant Tea Partiers themselves) will mostly agree with.

We know that they want to "go further Right" (although there hasn't been too much further they could go for a long time now), and they welcome that assessment that they _do_ want to be a very pure Rightwing party.  And what you say about Lindsey Graham is also very fair, and seen with equal clarity by both reasonable America (us) and the Fringe Right lunatics (them);  that 90% out of 100% Conservative rating is not nearly good enough for them.  Go ahead--look for any Rightwing site (or one of these trolls) who will defend the honor of 90% Conservative Lindsey Graham. 

The thing you miss, however, is that the "moderate" part of the coming Republican "split" is dead before it starts.  There aren't virtually any nationally electable moderate Republicans anymore.  Even if you add a handful of Conservative _Democrats_ and envision them as moderate Republicans in the near future, there _still_ aren't very many.  They will get virtually no funding by what is now (before the split) the GOP Powers-that-Be, because all of the energy will continue to be for the Tea Party idiot candidates, and they will regularly massacre the "Republicans" in the primaries or in the general elections.  The result of all of this will be (if your future holds true), a very short-lived GOP split, and then a coalescing back into complete GOP hegemonic power of only the fringe far Right.  There will be no survival of that thing formerly known as a "moderate", and the Castles and Schwartzeneggers and Caos and Snowes and Crists of the world will  all retire without any heirs.

As for your last paragraph, the GOP _have_ asked this question, and it wasn't just during the passage of the stimulus bill--it was in decent part after 9/11, in large part after Bush debacles in 2005 (Harriet Myers, Katrina, etc.), and in overwhelming part after Sarah Palin's convention speech.  People were saying the same things about the failure of Obama's presidency and the need for revolution in December--BEFORE he took office.  They have asked the question, and they have answered it.  For better or for worse, their path is DECIDEDLY to go further and further Right until either their ironclad conviction to being self-destructive takes the country back or they fall off a cliff.