I think health care is just like anything else that is a product of someone. We pay what we can afford. I can't afford a million dollar house so I don't get a million dollar house. I can't afford a million dollar surgery so I don't get it. I don't see the problem. These things don't grow on a tree or fall from the sky so why would everyone have access to them. The history of health care, and every other product of man, is that things are expensive when they are new but the price quickly comes down so that more can afford them. But why would they be available to everyone? In order for some expensive health care treatment to be made available to someone who does not have the means to pay for it, it means someone who produced wealth must have his property taken away from him and given to someone who didn't produce it. For one man to have a right to something he did not produce, someone must lose his right to something that he did produce. That does not seem just to me. In fact, it is down right irrational. It would punish those who succeed, for succeeding and it would reward those who fail, for failing. If one is poor enough and fails consistently, then one has a mortgage on the life and work of others. But, if one works really hard, studies, learns and puts that knowledge to use creating wealth, he loses his right to it in proportion to the degree of his success, so that eventually he becomes rightless.
You speak of the resources that "we" have but it is really individuals who have the wealth. It's not "our" wealth.
The basic principle underlying your question is: From each according to his ability, to each according to his need. I think it should be: from each according to his ability, to each according to his production. "We" do not have a right to someone's property simply because he has more than "we" do. This seems to be the only rational basis for society.