Jonathan Chait has a nice one today in which he looks at GOP attempts to understand why Barack Obama is pushing tax increases on the rich. The gist of it is that it apparently doesn't occur to Republicans that Democrats might support higher taxes because it would reduce the deficit (or, to put it another way, because it would fund programs Democrats support).
This, of course, is recognizable as the GOP war on budgeting. Under war on budgeting thinking, each tax and each expenditure is evaluated in isolation as good or bad; there's no sense that one needs to compare one expenditure to the other, or to revenues, in order to get the whole thing to balance. At best, there's a sense of "is this worth the money?" kind of question...you'll hear conservatives say that some program would be nice, but isn't worth taxpayer's money. But there's no sense at all that one needs to consider any expenditure in the context of all expenditures. Of course, advocates in general try to talk that way about programs they like -- but war-on-budgeting conservatives do it in the context of deficits and budgets.
As far as how deeply Republicans "really" believe it...the best way to deal with that is just to realize that the war on budgeting frame helps explain what they say and do really well, and that's good enough.
As it is in this case: the idea that Democratic support for higher taxes as part of a solution to a deficit that's too large -- that Republicans loudly insist is too large -- is something difficult to explain is, really, pretty weird. It doesn't need a complicated political explanation! Of course, given a choice between raising taxes on rich people and, say, cutting Medicare, one would predict that Democrats would choose raising taxes on rich people. It only needs an explanation is it doesn't occur to you that choices of that kind are necessary when budgeting.
Of course, we could always conclude that Karl Rove and the others who Chait quotes are just making up a phony attack just because partisans do that. But the nature of it, I think, shows that the really do find this to be something rather puzzling on policy grounds and therefore in need of some other explanation.