I don't think anyone's arguing that there's a fundamental right to all possible health care, but many people would argue that all have a fundamental right to basic health care, which is absolutely possible to offer to all Americans. In fact, many other countries do it while spending less per capita on health care. Of course, there are hard decisions to be made, but the status quo seems worse to me by a long shot.
My concern here isn't the breadth (who is covered), but the depth (what and how much is covered). That is, regardless of the number of people we're covering -- whether it's everyone, or excluding the poorest 20% who can't afford insurance, it is impossible to cover every conceivable treatment.
Consider, for example: a headache could be a symptom of brain tumor or other problem, the best diagnosis of which would be through an MRI. We'd like to catch these things as early as possible, so we'd like to do MRIs on everyone who is a possible victim. But imagine that every time a patient walks into the doctor's office with a headache, the doctor orders an MRI for him. How long do you think this practice can be sustained for?
The fact is that in a world with scarce resources, we must make decisions about how to allocate those resources. When the field of medical care is controlled by politicians, then politicians will be making those decisions. The questions over who is covered for what maladies with how much treatment becomes a political question.
So you can expect that maladies that cluster on easily-identifiable demographic groups will receive a disproportionate amount of funding. For example, one might expect that because gays may comprise a voting bloc and suffer from HIV more than others, politicians will pander to them for votes by allocating funds for HIV treatment that are out of proportion with the number of sufferers and the severity. By contrast, other maladies -- say, my Crohn's disease, which has weaker demographic ties -- are likely to be relatively overlooked.
And in the end, although the GOP is certainly using hyperbole in referring to "death panels", someone is going to have to make a decision at some point that treating this 90-year-old geezer just isn't going to have the ROI in terms of quality-life-years saved, and that it's not cost effective to continue treatment.
Anyway, my claim is that when the politicians can decide what and how much you're getting of something, it's difficult (in my mind, at least) to call something a "right". What other rights do we have for which the politicians get to make the decision about how much of that right each of us is entitled to?
Firstly, I don't think your hypothetical qualifies as basic health care. I understand your concerns, but they just don't seem to be huge issues in the countries that actually have implemented universal health care, especially compared to the current situation in the US. Getting caught up in the semantics of where your rights start and end (by the way, many rights are regulated by laws created by politicians) is a distraction from the pragmatic approach of looking at expected outcomes.
I don't think your hypothetical qualifies as basic health care.
And there is the problem. Someone has to make this judgment call. It's all a matter of opinion. And it changes over time, there's no single objective answer. Today, "take this Z-pack and keep the wound clean and dry" is a completely ordinary treatment; a century ago it was sci-fi, that wasn't even available to the hyper-rich. When does it cross the lines from experimental to esoteric to mundane?
by the way, many rights are regulated by laws created by politicians
That's only sort of true, at least in the USA. If something is understood to be a right, then those regulations are limited to only what can clear various tests as defined by the courts. Enumerated rights like speech, for example, are protected by a strict scrutiny test; at the other end of the spectrum is the rational basis test.
But in the end, these are actually judged by the courts. In other words, it's ultimately the non-political branch of the government that makes the call.
By contrast, these positive rights are entirely driven by political caprice.
(Caveat: I'm referring to Federal regulation here. It may vary somewhat state-to-state, because of how state Constitutions are designed.)