Like most of our legislators I have not read the bill in its entirety. :P
I would imagine that such a provision would have major 1st Amendment problems (religious freedom). On the other hand, with the insurance being administered via private companies the 1st Amendment argument may be weakened.
The thing that concerns me is the massive database of our health histories (compiled in one place). Once that system is set up who knows what abuses will or could occur. It sounds like a wonderful idea on the surface; however, I can imagine that it will make it very easy to mine data, locate non-compliant people, etc. Perhaps at some point you will not be able to access public places unless you've had your flu shot (or any of the 30+ other vaccines/boosters). At least in that scenario "public health" won't ride almost solely on our children's and babies' shoulders like it does now (not that I agree with it).
This is one of those issues that can have far-reaching consequences. I will be watching to see what happens, and I will be prepared to object (peacefully and within legal means of course) to usurpations of our individual liberties.