To be honest, I am unsure.
On the one hand, I would say no, the government should not be forcing someone to buy a product simply because they are alive (major difference between car insurance - you are only mandated to purchase it if you choose to own a car).
On the other hand, what is to be done with people who choose not to purchase insurance, but then need medical care and cannot afford to pay for it? Are they turned away and left to get sicker and die? Should the doctors be forced to treat them without compensation? Neither seems right. Does the government pay their bill? If so, then why not just require them to have insurance in the first place?
And around and around it goes.