Constitutionality of government obliging you to make a purchase v. taxing for it

[Nym90]

Taxing you to pay for a government-run health care system would be much more of an inhibition on personal liberty than requiring you to purchase it from the private market, since at least in the latter case you have your choice of providers. So it makes no logical sense to me that the former is constitutional and the latter isn't; if the federal government has the power to tax, that to me implies that it has the power to do anything that is functionally equivalent to but less restrictive to personal liberty than a tax.