I am not too sure what you mean here, but who you make the check out to matters A LOT. The government does not play by the same rules as the businesses they would be 'competing' against. They can afford to run at a loss because they have taxpayer backing. Moreover, doctors already have to charge private insurance companies more for services because they get paid less from people with Medicare. Put more people on Medicare (essentially) and doctors will have to keep raising rates on private companies, which means they have to charge more to consumers. It's a pretty quick way to drive private business out. So then we have socialized medicine. I wouldn't want to compete with a government lemonade stand that sold their product below cost.
There are certainly valid arguments for universal coverage, but you fail to mention the inevitable rationing. It has been mentioned that it is a fact that there is a longer wait in Canada and Britain for medical procedures. Why do we think we would be able to avoid that fate? We don't have enough doctors as it is. Insure everyone, and pay less for each doctor visit, and we will really be in trouble. Some people are willing to make that sacrifice, and that's OK, but I am not.
I don't think it has been brought up on this thread (I misses a few posts, I may be wrong), but people also forget the impact on our drug industry. We often hear complaints about the high cost of prescription drugs, but thanks to our patent laws, some 90% of new drugs are developed in the US. Many other countries offer the same drugs cheaper because they ignore patent laws and produce their own generics. If the liberals make good on their promises to go after 'windfall' profits (as Mr. Waxman has declared 'equitable') of pharmaceuticals, cures for cancer, diabetes and male pattern baldness will be pushed back many years. It is a pretty solid law of economics: if you want less of something, tax it more - do we want fewer drug discoveries?