I first heard that question in the 2008 presidential debates.
I'd never really thought about it in those terms, and I wasn't quite sure how to answer. Since then, we've seen that question in many forms and forums, and, though the left usually declares health care a right (with caveats to be discussed below), the conservative answer has been mixed -- some say it is a privilege, and some say it is a responsibility.
My initial response to the question was to say that it was a right, but then I balked because, as Dr. "Dalrymple" put it, "If there is a right to health care, someone has the duty to provide it."
But if it is a privilege or something else, then no one has a claim to any care at all -- a notion we rejected as a society long ago.
I believe health care is a right.
If we have a right to life -- as our founding documents have said and as we have derived from scripture -- then we should have a right to what is necessary to maintain that life.
But that does not mean someone has the duty to provide it.
To understand why, consider another right, that of free speech. Our right to free speech does not mean that anyone is obliged to publish your book or put you on tv or even to give you a laptop and a blogger account.
A right to free speech means government can't lawfully silence you, prevent you from spreading your ideas.
A right to health care does not mean that anyone is obliged to pay for your medical care. It means government cannot deny you care because you're black or gay or a member of the wrong political party (think USSR). What about "because you're poor?" Denying you care because of your socioeconomic status is not the same as not providing something for free.
We all have a moral obligation to love our neighbors, and sometimes that means helping the sick or the hungry. We can, as a society, decide that we want to handle that corporately, e.g., to create government programs to do it, but that is not because health care is a right, nor does it make health care a right.
That liberal caveat:
Liberals will generally say health care is a right, but they don't mean it, at least not in the way they claim.
As shown in the countries with nationalized health care (e.g., Great Britain) and in the bills currently floating around Congress, they don't believe health care is a right. They believe health care is a privilege you are granted as long as you aren't too old, too sick, or in need of expensive medicine. If you are, then government is, to them, well within its rights to cut off your health care and help you suffer or die quietly -- which ever way you want to think about it.