I'm no expert, but I think:
Health insurance needs to separate from employment. "A public plan takes away our right to choose our coverage." Bull. If you're like me, you don't have any choice about your coverage now--you get the plan selected by your employer. Your job doesn't provide your auto insurance or your homeowners/renter's coverage, why should health coverage be any different? Employers benefit not only from not having to provide coverage, but from eliminating the people needed to administer and shop for their programs. Less money needed for benefits means more money for salaries.
A public plan doesn't eliminate private coverage. Take Medicare for example; you still need supplemental coverage for what Medicare does and doesn't pay.
How about this? Use Medicare as a model, and cover all citizens with a limited, basic plan. Allow individuals to purchase their own supplemental health coverage, just as they now do for anything else they insure. Competition results in improved plans
Can't afford the supplemental insurance? You can still see a doctor without going to the ER (probably the most expensive way to see a doctor now). The doc still gets something from your basic plan. And if you set up a method for doctors having medical school loans reduced in exchange for treating those patients, I bet you'd not have much trouble recruiting young docs.
Surely there are problems with this. So what am I not taking into account?