But the government has made certain innoculations mandatory the DPT, Measels, and Polio vaccines were all mandatory to attend public schools in California as well as the old small pox vaccine.
Yes, the gov probably has the power to force it. I dunno', though. When they legislated it in the past, people had polio very much on their minds, without today's complacency about diseases that have been all but eradicated. As for the infant injections, there is little opposition and a strong constituency for it.
But like VietNam, it may be that passing the law (entering the war) is much easier that prevailing once opposition is mobilized. Bad analogy, I know, but you get the point.