You can't make me

Whether or not the individual mandate in President Obama's health care bill will be deemed unconstitutional by the US Supreme Court is yet to be seen.  To be completely honest, I have no idea if it's constitutional or not.  It would seem that compelling someone to purchase, on the open market, a privately offered product is something entirely different from something that is provided openly by the federal government and available for all to use, the cost for which is paid for out of general--or specifically earmarked--funds.

Take driving for example.
The feds can't require people to drive on roads.  However, they can levy a general tax on gasoline that provides funding for highways thus lowering the cost to travel between cities on roads.  Consequently, people transition from traveling long distances by rail to travelling long distances by roads.  You can choose to drive on (presumably quicker) toll roads, or take alternative transportation such as trains or planes or nothing at all, but you wouldn't have to.
If the feds used the same model for health care, there would be a general tax levied for health care, then a program to provide insurance back to the populace.  If you chose to buy (presumably better) insurance on the private market, you could do that.  If you chose not to purchase private insurance, then the government program would be the default.

That program would likely work.  They kind of already do that with medicare.