Is universal health care (not just emergency health care) a fundamental right in which all are entitled and the government should provide (on the tax payers dime)?
I would have to say no.
In America you are generally expected to generate some amount of income which will then cover the expense of the resources that you use being alive (i.e. food).
For example, in general people expect you to pay for your food. Although good health care is important over the long term, food is important over the short term. Some organizations give food away for free (In Houston I heard that a homeless man can get three free meals day if he is willing to walk for it) in the name of charity, but that is not the norm. And in those cases where food is given away free it might come with strings attached.
I don't see how health care is any different than food. Except the democratic socialists are trying to get me to pay for the health care.