Would a "public plan" destroy private health insurance?

From an op-ed piece in the Miami Herald :

“As work begins in earnest on health reform this week on Capitol Hill, Democrats are hoping” to create “a government-run insurance plan to compete against private insurers.” If that happens, “private plans will soon find themselves in the same perilous predicament as Ford Motor Co.: the federal government has stacked the deck against them.” Gingrich and Merritt say that the “main argument for a government plan is that private insurance is too expensive, and in order to expand coverage, Americans need an affordable alternative.” Therefore, “a government plan would have to dramatically under-cut private plans on price.” They also maintain that “destroying the private sector in health would replace competition and consumer choice with bureaucratic power and planning. There would be no incentive to improve quality or increase efficiency — but every incentive in the long term to control costs by restricting access and choice.”

I’m not convinced the insurance companies are completely unhappy; someone has to “run or administer” the health insurance itself (under the over-all direction, of course, of government bureaucrats). But, long term, it’s hard to see how a gov’t-run plan doesn’t restrict choices & options for most folks. Government plans already account for over half of health insurance (Medicare, MediCaid, & government employee plans): if the government would be so much better at controlling costs, why haven’t we seen it yet?