I want universal health care because it's a universal human right.
I'd like to explore this issue more. Is it really a universal human right? It sure would be nice if everyone got health care. However, people provide health care, and I don't think any one has a right to demand anything out of those people. Rights (I think) ought to be things that you have a right to do, not a right to have someone else do for you.
For example, free speech means you can say whatever you want, but you do NOT have a right to an audience. The 2nd amendment acknowledges the right to bear arms, but it does NOT mean that someone has to make, assemble, sell, or provide you with said arms. You do have the right to peacefully assemble, but that does NOT mean you have the right to peacefully assemble on someone's private property.
Health care, on the other hand, universal or not, is vastly different. By saying everyone should have a right to health care, you are saying that everyone has the right to demand someone else to provide them with something. I think that's a dangerous path to go down.
However, things can get a little muddled with, for example, the right to a fair trial. The 6th amendment states you have "...the right to a speedy and public trial, by an impartial jury...", and that means you have the right to force others to be speedy, public, and impartial. However, in that case, if your trial can't be speedy, public, or have an impartial jury then you should be let off without a trial. Which means that a right to a fair trial is still different than health care as a right.
Again, I think it would be nice if people got the health care they needed. However, I don't think we ought to go down a path where we say that someone has the right to another person's time and resources.