The US healthcare system is broken on many levels, and I don't think anyone has the balls to really fix it.
Some ideas:
[1] Free basic medicare for everyone, but allow people to pay for faster/better service. This is the way it works in the UK, and it works very well. The basic service is fine for most people, but if you want a room to yourself or you want to jump the queue, you can pay to get US-style service. Overall it works out much cheaper and fairer than the US system.
[2] Set up a system that allows uninsured people to get the same rates as the insurance company. It's a bit of a scam at the moment - basically the hospitals seem to be out to screw you if you're not insured.