This article in The New York Times offers some detail on the government-run insurance plans at the state level. I learned:
1. Three dozen state governments currently run such plans and they do not in general drive private insurance companies out of business. In California, the largest such plan, two-thirds of all eligible people choose the privately-run health insurance plans.
2. The state-run plans are usually administered by a major private insurance company, which has authority to negotiate payment rates with doctors and hospitals. In this regard the forthcoming Obama proposal might be quite different.
3. These plans are not especially effective at controlling costs.
4. The North Carolina plan now requires a significant bailout.
5. Some people (this is now my esoteric reading) view the state-run plan as a way of forcing private insurance companies to bargain down reimbursements much further than they have done. It's a monopsonistic social means of opting for lower expenditures and lower returns for the medical sector.