In the comments on my health care rationing post, I received many standard attacks as being cold-hearted and willing to deny health care to people who need it.
From a libertarian perspective, your generosity is reflected in what you do with your own money, not in what you do with other people's money. If I give a lot of money to charity, then I am generous. If you give a smaller fraction of your money to charity, then you are less generous. But if you want to tax me in order to give my money to charity, that does not make you generous.
I believe that some health care ought to be provided collectively. I would like to see people who are very poor or very sick receive health care. Are taxes required in order to get this result? Perhaps. But perhaps not.
Think of government as a charity. From a libertarian perspective, it is a charity run by the Mafia, which will break your knuckles if you don't make your donations. It is also a badly mismanaged charity. It funnels lots of money into questionable causes, and even when the causes are good the programs that it funds tend to be very wasteful.
I would like to see government have to compete with other charities on a level playing field. I often say that government should have had to fund the financial bailouts by holding a bake sale.
In an environment with a level playing field, perhaps charities that provide health care to the very poor and the very sick would be better funded and more effective than the existing government programs. If that did not happen in practice, then I might support the Mafia-run charity that we call government.
But being libertarian does not mean you have to have a cold heart. You can be a bleeding heart, but you show it by what you do, not what you advocate forcing other people to do.