I don't have the studies in front of me, but it generally depends. In the case of diabetes, for instance, a lifetime of diet monitoring and counseling by a doctor or nurse is still way cheaper than insulin or amputation.
The diabetes example is not one I had thought of, I'll look into it.
What bothers me is that I see a lot of knee-jerk "we'll just make it up on preventative care" in the debate, without any way of proving how the costs add up.
Without having looked into it deeper, my question about diabetes would be whether free/cheap checkups and counseling affect the number of people who correctly handle their problem.
There's a pretty clear medical consensus (based on tons of data) that diet and exercise affects the development or progression of diabetes (well, type II). There's also a wide consensus that professional counseling and monitoring helps (though I believe it's harder to get really "clean" studies to support this, since you'd need a control group of people who you monitor closely enough to get good comparison data without actually talking to them about what's going on).
The follow-up question, of course, is whether (or how much) the cost of checkups/counseling affects whether/how much people seek it out, or whether that behavior is more idiosyncratic (i.e. "some people just don't care about their health, so even if checkups were free they wouldn't bother").
To be fair, I haven't seen any study that conclusively proves the issue (which of course doesn't imply that one isn't out there). However, if we're really going to make the claim that economic incentives don't matter, then we really need to question a lot of other assumptions as well. I'm pretty comfortable saying that at least on some level, to some degree, economic incentives have some impact on people's behavior in seeking care.
In terms of "we'll just make it up on preventative care", I agree, that's not a panacea. At the same time, a lot of the money that's slated to be spent on covering the uninsured is still spent today, just in really stupidly inefficient ways.
For instance, because you generally can't be denied emergency room care, people without insurance often end up using ERs as primary care. Because ERs are primarily meant to handle, well, emergencies, the standard of care is generally more expensive than a clinic or "regular doctor" (this means things like faster and more expensive tests, drugs, and so forth). Many of those people simply can't pay, but the hospital treated them anyway (which, just to be clear, is a GOOD thing - it would be a pretty horrid society where we let people bleed to death or what have you). Many hospitals would have a hard time staying open if this went on indefinitely, so the government reimburses them for this uninsured care.
So, at the end of the day "we the taxpayers" still pay for a good deal of uninsured care... we just do it via an indirect subsidy to hospitals for expensive ER care, rather than paying directly for (much cheaper) clinic care, or something along those lines. As with most things, the less directly we're tackling the problem, the more inefficiency there is in the system.
It would be foolish to claim that all the costs of a big health care/health insurance overhaul would be paid for by money already in the system - clearly, that depends a great deal on the details. But at the same time, it's important to remember that some of the money can come from within the system: at a minimum, if we reduce the number of uninsured people, we can reduce payments to hospitals for uninsured care.
It's not a zero-sum game - electronic medical records and that sort of stuff aside, there's a lot of honest-to-goodness inefficiency and perverse incentives in the system, and that's what (a good) reform ought to tackle.
Edit: just to be clear, reimbursements for uninsured care take many forms, and there's another, more obvious one: higher prices for everybody else. The salient point is that much of this care is being provided anyway, so why not do it more efficiently?