Federal government mandates for health insurance violate the Constitution in several ways.
The most obvious is the Tenth Amendment: Congress has no authority, implied or expressed, to force everyone to get health insurance. Therefore it cannot do it. And no, please don't say "general welfare," as this was never intended to be a grant of power, but a description of the powers to follow in Article I, Section 8. And no, please don't say "regulating interstate commerce," because regulating commerce is not similar to forcing everyone to engage in a particular commercial act.
There's also the Fourth Amendment. I have the right to be secure in my papers: the government has no right to know if I even have health insurance.
Then there's the Fifth and Fourteenth Amendments: I cannot have my liberty taken away from without due process. This is admittedly the shakiest of my claims for historical reasons, due to the unfortunate slippery slope of history, but it seems to me that I should have to be proven to have done something wrong in order to have my liberty taken from me.
Perhaps the strongest claim, however, is that the First Amendment guarantees the freedom of association. The Supreme Court has held that this necessarily also implies the freedom to not associate. If I dislike all insurance companies and choose to not associate with them, that is my constitutional right. Similarly, I may decide that having insurance (entirely, or when I have more important uses for the money, such as donating it to an anti-sex slavery charity) is against my religious beliefs.
Cross-posted on <pudge/*>.