The biggest problem with Universal Healthcare is the money. Sure you can say the government has spent more money on less important things, however, in this case, it isn't the government who takes it the hardest. The problem with Universal Healthcare is that it takes away from the doctors! Being a government organization, the doctors will get much less pay, affecting the quality of their care.
You can say 'why don't doctors just go into a private company?' It wont work! Private hospitals are going to get a lot less patients and will lower their funds. And again, doctors are in the same situation.
Ok, maybe the choice between universal healthcare and your own healthcare is the best solution.. No. The fact is is that there will be NO choice! Most people pay for there healthcare through their jobs. For instance, I have had a fantastic plan with Kaiser for over 3 years through my current job. They sat us down recently and told us that they are cutting our 401k and lowering our health insurance simply because it is cheaper and they need the money. If the universal healthcare plan goes into effect, there will be no hesitation to switching to the government funded plan.
Everything will fall back down to government funded health because it is cheaper. Private hospitals will fail and completely vanish simply because there wont be enough patients to keep it running.