From The New York Times:

But the law depends to a significant degree on the mandate. Without it, some healthy people will wait to buy coverage until they get sick — which, of course, is not an insurance system at all. It’s free-riding.

Without the mandate, the cost of insurance in the individual market would rise, perhaps sharply, because some healthy people would not be paying their share. Just look at Massachusetts. In 1996, it barred insurers from setting rates based on a person’s health but did not mandate that individuals sign up for insurance. Premiums then spiked. Since the state added a mandate in 2006, more people have signed up, and premiums have dropped an average of 40 percent.