Yeah I kinda hate the entire notion of universal health care because it takes a bad system and makes it worse. You see, the biggest problem in the American health care system is insurance. Doctors often order more tests than what might be necessary to detect the suspected problem, number one because it is far too easy to sue doctors in todays world, and number two because insurance pays for it not the patient. They will also often prescribe expensive medications when a low cost generic alternative is available, again because insurance pays not the patient. This unnecessary cost on the insurance company is directed immediately to the insured in the form of higher rates. This of course makes it harder for poor people to get insurance. So, you end up with poor people who can't afford insurance that just keeps getting more expensive.
Well, imagine if not even the insurance company had to foot the bill. Not even a deductable to the patient! Rates can never go up because of a claim... Well you can see how this just prompts doctors to prescribe more expensive medication and perform more expensive tests. In addition, now everybody can afford to go to the doctor for everything! Sounds great, until you actually need to see a doctor for something serious at which point you realize that every office is overbooked and impossible to get into in a timely manner. Oh, and don't forget that doctors in countries with universal health care tend to make less money(varies from marginal to quite substantial amounts) so less people want to become doctors thus exacerbating said problem.
So how do we fix it?
A great start would be to cut costs in the two areas outlined above. If every doctor worked with the goal of keeping the medical care as low cost as possible for not only the patient but the insurance company as well, then perhaps we could get rates down to a manageable level for everyone.
Emergency rooms also really hurt hospitals financially (forcing up costs elsewhere), mostly due to the fact that they don't refuse treatment so those without health insurance will sometimes use them as a free clinic. Just come in, get treatment, and walk out on the bill. This problem is a bit trickier, for obvious reasons, but it needs to be addressed as well...