The entire pro-choice movement is based on the concept of "My Body My Choice". You start forcing people to accept injections of anything into their bodies and you lose the moral basis for that argument. How do you "force" people to accept vaccines? Strap them down and inject them? Could anything be more frightening than the government forcing chemicals into someone's veins? That will make people even more anti-vaccine than ever.
I'm am very pro-vaccine. From childhood illnesses to flu to hpv, I want them all for myself and kids. And I have gotten into arguments with ignorant anti-vaccine people. What I have found is that they simply have lost all faith in "authority" because they have been lied to time and time again. WMD in Iraq! You can keep your insurance! Eat the food pyramid because you need to eat twice as much bread as you do veggies (not kidding, look it up). Leaders lie and lie and lie again to get what they want. Is it any wonder why people don't believe anything. In fact, it seems like the more forceful the denial the more likely the lie. You try and make vaccines mandatory you WILL make a bigger anti-vaccine movement.