Constitutionality of Obamacare

Is Obamacare constitutional?  Georgetown University law professor Randy Barnett, writing in today's Washington Post, has some doubts.  Here's a key 'graf:

But the individual mandate extends the commerce clause's power beyond economic activity, to economic inactivity. That is unprecedented. While Congress has used its taxing power to fund Social Security and Medicare, never before has it used its commerce power to mandate that an individual person engage in an economic transaction with a...