Yes. Unfortunately, that is impossible in a country where the wealthy refuse to treat the masses fairly by sharing the wealth. Most of our citizens cannot realistically afford healthcare, while still having a shot at the American Dream of improving their lot in life. A quite sizeable chunk of the millions of reposessed homes have been a direct result of unmanageable healthcare debts. That is why most otherwise capitalism-based countries have what you call socialized healthcare. Universal healthcare is unattainable in a strictly Capitalist society.
You do know the wealthy already pay most of the income taxes in the United States as it is? the masses are there for a reason. They have no shot in the american dream if they want to live off the success of others.