Well, I'll weigh in on the other, unpopular side of the argument and say that there would have to be many utterly massive changes to move to a universal health care system in the US. And these changes wouldn't just affect the US--they'd affect much of the rest of the world as well.
Medicines developed within the US are sold at higher prices here than they are abroad. There is a definite profit motive to the development of new medicines--and there pretty much has to be, as most medical trials fail due to either the drug not being very effective or, much more commonly, the side effects being too severe to warrant the use of the medication. Given the large amount of time, energy, and money that must be poured into the even getting a medicine to an FDA trial, let alone getting one through and to market, most companies will only take the risk if they can expect a hefty financial gain on the ones which do make it. Lowering the costs we pay for medicines here will either need to come hand in hand with raising the costs of medicine in other parts of the world, or a recognition that there will be fewer and fewer need medicines developed as the incentive for corporations to do so goes away.
There will always be a shortage of medical care unless you're willing to push taxes well beyond the 40% or so that the countries with the most socialized systems of medicine have. In the US, rationing takes place largely based on financial ability to afford the treatment. In countries like Canada, rationing is more temporal. Last time I checked the stats on a heart bypass in Canada, waiting time averaged approximately 6 months, which coincides with approximately 50% mortality for those needing a bypass. In the US, if you can afford it, you get your bypass the next day..or maybe after a two or three day wait if there happens to be a holiday or a lot of other people getting the procedure done just then.
Many people quote that money is the root of all evil. That's an incomplete quote--the actual passage is that love of money is the root of all evil. Money is an inherently worthless thing, and only has value for what it can gain you. That includes basics like food and shelter, luxuries like air conditioning (which I wish I had with this heat wave), and freedom from certain types of worry such as "how will I put food on the table next week". While I can see the argument that basic medical care is a right, much of what we think of as standard medical care is really something of a luxury. I don't see well on my own, so I go to the optometrist and get a pair of glasses, and I can see better. My head hurts, so I take an aspirin. A friend's joints hurt, so she gets arthritis medication. My father had a TIA a few years back, so he takes a daily blood thinner to lower the odds he'll have another one. Many of these things really are more of luxuries than necessities, and that gets even more true as we move into old age and our medications are fighting against basic biology. Why are these luxuries ones where it is not acceptable for money to determine who has them and who doesn't? People can certainly get into significant financial hardships, but most of the time when things are available for purchase, the consumer is making choices about how worthwhile it is to him/her to make that purchase as opposed to another one. Since people have different risk tolerances, some will opt to protect themselves against possible medical disasters, while others will gamble that they won't need such protection and will spend that money on a nicer home or more expensive food or whatnot--and it is their choice to do so.
If we make a move to universal health coverage, we'll have three options: 1) Make a list of those treatments/conditions which are treated, and those which are not, based upon a cost/benefit ratio and an assessment of how common the condition is. Of potential note to this community--there is basically no chance of any AIDS treatment ever being covered this way (though research on a vaccine might still be funded), as even though antiretroviral cocktails have extended lifespan the disease is still virtually 100% fatal. 2) Massively increase taxes. 3) Accept a luck of the draw waiting system, where even if your treatment is covered you'll have to wait long enough to get it that there's a reasonable chance you'll die in the meantime, with basically nothing you can do about it. And these three are not mutually exclusive either.
Universal coverage for children may be politically viable in the US, but I highly doubt people will be willing to make the sacrifices necessary for a full coverage of the adult populace.