I think the best approach to national health care is to utilize the Pareto Principle.
To oversimplify, the Pareto Principle holds that approximately 20% of the population of something is responsible for around 80% of the traffic. If you have, say, 30 people on your cell phone contact list, you probably call 5 of them every day, the next 5 a few times a week, the third 5 maybe once a week, the fourth five, a couple times a month, the bottom ten, rarely or never.
In health care, there's a relatively small percentage of all the ailments out there that are the primary drivers of health care utilization. Minor injuries. Respiratory infections and influenza. Management of chronic conditions like hypertension, diabetes, thyroid imbalances, pain, depression and schizophrenia. Caries. These are conditions that are relatively cheap and easy to treat...yet have the potential to spiral into expensive, debilitating, even (in some cases) life-threatening situations if they are not managed.
This is what a national health care system should focus on: covering everyone for this 80% or so of doctor's office visits. This would keep the cost of the national coverage down, yet substantially improve the lives of the presently uninsured. It would also help serve to bring costs down, as it's a lot cheaper to treat a condition with a $50 office visit and a $50 prescription than a $2,500 ER visit.