I don't understand how this "everybody must buy private health insurance" is even possible. So, someone making $20,000 a year is forced to buy private insurance. Three months in they realize there's no way they can pay for it and keep the lights on and their kids fed. They default on the payment and the insurance gets canceled. What's the government going to do, come out and arrest them?

This could work if employers were forced to provide insurance, but that would completely stifle small business.

The only solution is a single payer system.