The powers not granted to the States specifically are either concurrent powers with teh Federal and State governments or are in fact granted exclusively to the people.
States Rights are specifically provided for in the US Constitution, but the hierarchy of law is as follows (each one trumps those listed below it).
US Constitution
Federal Treaties
Federal Law
Federal Regulations
State Constitution
State Law
State Administrative Codes
Local Ordinances
If it were determined that health care were a Right of the States, then there could be no Federal mandate for it; however, Public Health has long been recognized as a Federal and concurrent Power, so the argument would be difficult or impossible to pursue in court. For example, Public Health Nursing is mandated by the Feds and funded by them, but 45 CFR requires it be carried out by a State Giovernment or a local government under State Supervision.
I know you probably did not want a lesson on how a bureaucracy works on paper, but there it is. The answer is a resounding NO. A state most probably could not opt out on a Federal Health Care Program.
But I think you will discover you have less to fear than you think. Countries with essentially socialized medicine are beating us in terms of the overall health of their populations. In most of those countries, Doctors are still paid well, but they cannot in general become tycoons from a medical practice alone.
There are companies in this country already managing care for the chronically ill to keep the cost down, and not only are they successful, but generally their clients' clients. (Those who are having their care managed via automated processes by virtue of being insured by a participating company) also live longer.
And there are other areas where profit is not the driver of inn9ovation most tout it for, such as the auto industry.
But it won't be Obama doing the Health Care. That is not a Presidential power. It will have to be done by Congress, if it is done at all.