First of all, I should let you all know I'm not interested in debating, so I don't intend to respond to any replies. I just feel that the libertarian position on the issue has not been properly represented in this thread. Please don't make the mistake of thinking your existing beliefs are infallible. If I present information or ideas you've never heard of or seen explained well, research it properly. Whether you find you agree with me or not, you owe that much to yourself.
Libertarianism in America, as you likely know it from TV, is a philosophy of "every man for himself." That's totally wrong. Real libertarian philosophy is based on the non-aggression principle. It is an opposition to coercion and the use of force, except for defensive purposes. That includes coercion by government when it attempts to do things that would be unacceptable for private citizens to do, such as taking someone else's money without consent (taxation) and attacking or imprisoning those who have not harmed others.
It is the belief of libertarians that the free market, when self-regulated by its active participants, provides better solutions to problems than any government could hope to achieve. In the case of health care, we have observed how government intervention has caused prices to increase and the quality of services to decrease at every stage.
In the years before Medicare and Medicaid were introduced, poor people were admitted to hospitals and granted care across the US at the same rate as they are now. However, back then, it was accepted and understood that not everyone was capable of paying for their care. You know what doctors did about it back then? They did it for free.
After adjusting for inflation, prices for health care services were still only a fraction of what they are now. Government intervention and the rise of government-sponsored health insurance (HMOs are the best example) caused a systemic increase in costs because it complicated the system and added a lot of new bureaucrats to the mix who all had to be paid for every person's health care. Insurance companies are also prohibited from selling their products across state lines, which keeps the biggest (and most well-connected) providers from being undercut by more efficient competitors.
On top of that, government deals with pharmaceutical companies stifle competition and allow those businesses to run roughshod over their customers, putting unsafe products on the market at exorbitant prices, which often cause side effects that require even more expensive drugs to suppress.
There are a lot more instances of government corruption and collusion with private enterprise in the health care industry for mutual gain that you should be aware of, but I'll just start to wrap up now. If I got your attention, hopefully you'll do some more reading on your own.
Governments are not impartial entities with the well-being of all their subjects at heart. They are composed of individuals, and those individuals, by the very nature of all those who seek power over others, are easily corruptible. Such people work for their own interests, and that generally boils down to solidifying, consolidating, and/or expanding their power.
Conversely, the people actually involved in the medical industry care about their patients. Very few doctors would want to let a patient go untreated, and if it were in their power to help poor people, they would. The problem is the layers of bureaucracy that stand between those in need and the charitable souls who want nothing more than to provide for those needs.
As a libertarian, I believe people want to be good, and if given the chance, most of us would be.