The answer becomes clear when we consider the kinds of "freedom" that the status quo – a lack of such government involvement – imparts. How many of us want the freedom to face medical bankruptcy, or the freedom to be denied coverage (and care) because of a preexisting condition? And how many of us see dying, due to lack of insurance, from a treatable or curable disease as an acceptable cost of individual liberty?
As with traffic lights, there is a trade-off; we cannot get something for nothing. The only way to have a system that guarantees necessary care for those in need – to give us the freedom to live our lives without that fear – is to make sure everyone is included in the system.
Broadly speaking, there are only two ways to do this: by requiring everyone to purchase insurance or by using a tax base to have government provide that coverage for all. There's an argument that the tax-based (single payer) solution might be even more liberating – but we need not make that argument here.
As for the notion that the new health-care law robs us of freedom because it is a mandate, let us not forget that we as a society created our government to make our choices and we used this mechanism to do so. This was an exercise of our freedom!
Freedom starts with the opportunity to make choices, including the choice of whether to act individually or collectively. A choice once made sets us on a more limited path – but are we not freer for making choices rather than remaining forever frozen in a prechoice world of possibility but no fulfillment?