To me, the first thing that needs to be done if to find some way to insure the uninsured. Adults who don't have it need health insurance of some sort. The problem is that most voters are middle aged or older and have some type of health insurance themselves. So why do something that's going to crowd your doctor's office with new people and raise your taxes besides?
The tipping point is most people worry about their children and their grandchildren. When enough middle class, middle aged, people have children who don't have health insurance, the uninsured will get health insurance.
The young man calls home from a phone booth in Denver. "Well Dad, I got a job!"
Dad: "Great! Does it come with health insurance?"
Mr. Mustache: "Duh, no, I'm contract labor."
Dad to Mother, "Well we're gonna have to keep buying his insurance till Mr. Mustache gets a better job".
Dad at that point would be a good candidate to become a supporter of health insurance for the uninsured. People will do things for their own they won't do for the neighbors across the street.