I think it's a fine line. It should be availabe, but not priced out of the range of affordability as it is now becoming. People shouldn't have to look to their employers to provide them with coverage. They should be able to seek an affordable policy on their own which doesn't take more than 30% of their income. The same guidelines used for affordable housing guidelines by the government (FHA).
They should also be able to choose some type of plan. Say they don't have much money, how about a preventative maintenance plan at the very basic for a small amount of money. For a woman, it could include a yearly checkup and gynecological exam with a basic dental exam and teeth cleaning. This could be made very affordable and give people more security than nothing at all.
If you ask most doctors, they would love to be able to provide basic healthcare. Just look at the free clinic/hospital projects which have been started not only in this country, but also around the world in the past.
Where the problems arise is for-profit insurance companies, hospital administration costs, malpractice lawsuits, and drug advertising.
All of these greatly increase the costs (overhead) which we pay, as a society, for healthy citizens.
The system is fatally flawed, but I think with proper legislation to control some of these overhead costs, it could be greatly improved. With even some very basic limitations, such as controlling TV advertisement for drugs, limiting malpractice lawsuit damage amounts, reducing drug patent time limits, and a national insurance program to ensure preventative care, things could be improved. Also, doctors shouldn't have to pay out the wazoo for building costs and taxes. I think any doctor who subscribed to a national insurance plan should receive some sort of incentive through tax breaks, etc.
Right now, medical students are at an all time low. With the current system, who wants to be a doctor? They are being squeezed by insurance companies and federal medicare/medicaid. There needs to be some choice. It's a big responsibility to be a health care provider. People shouldn't take it with a grain of salt, yet common sense on the health industries part needs to be utilized as well.