There are two things that proponents of public health care systems are loath to admit. The first is that they all ration care. As noted above, that doesn't distinguish them from a system in which care is privately provided, but the "rationing" that occurs in the latter is by agreement between the insured and insurer. People decide, either individually or through their employer, how much care - how much coverage - to purchase. It is true that these transactions are distorted in the US through operation of the tax code and that individual choices about how much to spend are distorted by heavy reliance on third party payment. The US does not have an efficient market for health care. But, however distorted (often by regulation and government policy), the nature of coverage (and the degree of "rationing" if that's even the right word to use) emerges from a market. Your employer provides chooses that degree of insurance that will attract employees and that can be justified by the labor market.
The advantage of this system is that it does not need to presume that there is an omniscient body (i.e., the government) that has the abililty to decide how much and what kind of care should be provided. President Obama's statement of an equivalence between "an insurance company" and "government" interfering in your health care is false. If an insurance company (or your employer) does not provide the type of coverage that employees want, there are other employers and other insurers. People vote with their dollars and that is what determines the degree and type of care.
The disadvantage of such a system is that it is affected by ability to pay and those without resources can be left to the sometimes less generous care offered by government programs and charity. (In the US, that problem is exacerbated by the fact of employer provided coverage - a system that is entirely a result of government policy.)
One way of solving that problem would be to subsidize the ability of those without the means to participate in the market. (In the US, the problem would also be helped greatly by migrating away from employer-dependent coverage.)But public health care goes beyond that, seeking to eliminate or further constrict the market. Either through a public payment or heavy regulation, it seeks to have decisions about the amount of coverage and what can be covered made by the government. Proponents tend to believe that this type of centralized ("top down") unsullied by considerations of profit will be "purer" and "fairer" than market decisions on these things.
There are at least two problems with this view. The first is that we know that government decisionmaking is almost never a product of disinterested consideration of the public interest. Just as market outcomes can be affected by the initial allocation of resources and incomplete information, political outcomes are affected by parties with more intense interests than the general public, the effectively opaque nature of much state decisionmaking and the self interest of state actors. (Thus, my frequent references to public choice theory.)
The second problem is that the notion that a single entity can decide what type of coverage is best and what forms of care constitute the "best practice" and are "effective" is highly suspect. Much of our back and forth about private and public decisions revolves around the relative competencies of public and private entities. But proponents of markets don't have to presume that any single market participant is competent. Markets permit - and even anticipate - failure. In addition, competence is forged from competition. Even the best intentioned human beings benefit from incentives. Every year, I see law students who really want to do well, but who only actually do well when they appreciate what it takes to match the competition.
Similarly, proponents of markets don't have to assume the public spiritedness of any market participant. As Adam Smith said, "[i]t is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest." Economic rent and sharp practices are disciplined and eliminated by competition and (I freely admit) by certain forms of regulation which permit efficient operation of the market (e.g., enforcement of contracts).
Of course, it is not true that public systems can be totally imperious and the public can provide a certain amount of corrective feedback (by, for example, voting the bastards out), but this participation is more indirect, delayed and attenuated than that of the market place. It takes longer to happen. A vote is a blunt instrument (markets permit thousands and thousands of choices, while elections only permit us to change a handful of people who are responsible for many things other than health care) and voters must make their infrequent and limited choice on many matters other than health care.
Of course, proponents of ObamaCare claim that he market will survive its implementation. Is that true? Watch this space.