According to this study there is another reason it would tend to shove private health insurance out of the picture. It has to do with the way in which the plan would combine government medicine with a certain feature of the present system, a feature that the study describes like this:
In today's system, hospitals and physicians provide a substantial amount of free care to uninsured people called "uncompensated care." Also, payments for Medicare and Medicaid are usually less than the cost of the services provided resulting in payment shortfalls. Hospitals and physicians cover the cost of uncompensated care and payment shortfalls under public programs by increasing charges for private health plans in a process known as cost-shifting.Since we can expect the "public option" -- a vast expansion of Medicaid -- to continue the same pricing policies, this will shift further costs to the shrinking number of people who still have private health insurance. This of course would increase the price gap between public and private insurance, driving even more people into the government medical system.
I expect the result would be a system in which the majority have crummy medical care but at low cost to them (until tax time) and a wealthy minority have much better care -- maybe something very much like the sort of care that most Americans have now.
This is why the town hall protesters keep mentioning the fact that members of congress will not be taking the public option for their own medical insurance. They all have private insurance now, and they are too wealthy to be driven into our part of the system.
Isn't it ironic? If you believe in equality and "fairness," the ideas the drive government health systems, you ought to be against this one!