The biggest problem with health care is that it costs a lot of money. The US is definitely overpaying medical specialists (specialists can make 4-5x the amount of a general care doctor) and procedures right now, but even if they were paying a fair price, the cost would still be a burden.
The old solution to this problem, as documented in Sicko, was just to screw the sickest people over and drop them from the insurance pool as soon as they tried to cash in on their dues, eliminating a large chunk of the financial burden on the rest of society. It should also be noted that insurance companies would end up setting their rates unreasonably high for the implementation of this strategy, resulting in a large suction of money into the companies.
The new solution to this problem with recent legislation is to try to force everybody into the insurance market, ensuring that the costs of healthcare are equally distributed. This is resisted because it means that insurance companies will have to raise their rates across the board to account for the increased risk of payout from the sick people they used to screw over.
There are a lot of opinions about quality of care changing, ease of access, etc. if the US goes towards a more universal system, but I think the central question is all about money:
Should 10 working class tax payers be forced to pay for an operation that will only postpone the death of a child by a few years? Should healthy people be forced to pay the bill for drug users and people that don't live a healthy lifestyle?
Should the strong be forced to support the weak?
The answer is usually "no" if you are in the strong group (18-30, active, hard working, no major health problems), and yes if you are in the weak group (40-80, working less, more serious health problems). In reality, it's not such a clean cut question, as the support has to be managed to make sure it is not being abused or ignored by either side.