For those who are really interested in health care and the budget, especially those who buy the idea that ACA savings are probably overstated because they depend on budget discipline from future Congresses, I highly recommend Ezra Klein's post today skewering Paul Ryan's Medicare plan. The gist of it is that Ryan's plan is just as dependent on budget discipline in the future in the face of prospective real cuts as the ACA is. So if you buy that criticism, Ryan's plan won't work either.
Of course, that's nothing compared to the GOP rhetorical strategy on ACA repeal, which is to specifically target the budget cuts included in reform as a front-tier talking point. And then there's the flat out myths (10/6, for example). And the whole doc fix thing—hey, does Ryan's plan count the budget expense of doc fix?
All in all, it's just really hard to take budget concerns seriously as the root of GOP opposition to ACA.
Unfortunately, it's a bit hard to figure out exactly what the basis for opposition is. There's the tyranny and constitutional objections thing, but see Jonathan Cohn's point last week about social security privatization. Perhaps it's just based on myth and falsehood (that is, opponents really believe that ACA is all about the death panels), but that presumably shouldn't apply to elite opponents of the law. There's the idea that it's all about opposing whatever it is that Democrats want, which is true enough—but doesn't really explain long-term opposition to health care reform, or why health care looms so much larger for conservatives than the other accomplishments of the 111th Congress.
My best guess is that it's bits and pieces of all of those, including at least some (mistaken but sincere, even if they're also willing to use arguments that cut the other way) concern about costs. The core of it, however, at least if I had to guess, is that ACA really is a “takeover” in the sense of really making affordable health care an absolute responsibility of the federal government. Such takeovers may or may not lead to expanding the size of government, or its direct reach into peoples' lives—since the late 1970s, liberal Democrats have shifted to favoring market-based schemes for liberal ends. But even if it doesn't expand the size of government, it does expand the size of government obligation. And that's a pretty big deal, and one that conservatives are quite right, from their point of view, to oppose.
To speculate a bit more...
The problem for conservatives, however, is that they've lost the game long ago: it is clearly impossible for a viable national party to argue that the government should stand by and do nothing if costs are exploding, if insurance companies deny coverage to large groups, if insurance companies do all sorts of outrageous things to their customers. How do I know that? Because Republicans, despite pressure from Tea Partiers who say that they want a very small government and threaten primaries to those who disagree, feel obliged nevertheless to accept government responsibility for health care, at least rhetorically. That's why they claim to want to repeal and replace, not just repeal: they are rhetorically just as committed to a government solution as the Democrats, even as they are also committed to, well, not doing that. Next time you hear someone make a fuss about polling that shows conservative self-identification far higher than liberal self-identification, keep that in mind: whatever people mean when they say they're conservative, most of them surely don't think that the federal government should have little responsibility for health care. Or, for that matter, the economy.
All of which (along with some opportunism, something that all politicians and all parties are guilty of) makes for some remarkably incoherent policy pronouncements.