Mitchell is absolutely correct that "coverage" is not the answer. Indeed, insurers are responsible for a substantial portion of the problem. A system in which private and public sources share the burden of providing medical care (note: not health care) to millions, where the private entities are driven by profit, is fundamentally biased against the most chronically and seriously ill and the impoverished. They are pushed into the public system, increasing profit for the private entities and wiping out the benefits of risk averaging for the public system.
I hope we can develop a system where we are caring for health, not merely giving drugs and doing surgery after health is diminished. As the population ages, the economic and social burden of chronic illness will expand. Chronic diseases require chronic care, and the occasional visit to the physician for a prescription refill falls far short of meeting this need.
What physicians call non-compliance (and nurses call a failure to craft a treatment plan the patient can carry out) can only be mitigated by caring for health problems. This means checking that those in need can afford their medication, have a safe home environment, understand their therapeutic regimen, are not experiencing side effects, know how to care for themselves to improve their health status, and so forth. This is the challenge of the 21st century health care system, and it is a huge one.