The benefits of vaccination for the receiver of the vaccine are usually enough to entice voluntary vaccination. In fact, I'm sure there are plenty of civic-minded people who get themselves (or their children) vaccinated for the benefit of everyone else, too.
The government would only feel compelled to forcibly vaccinate its citizens if people refused en masse to get vaccinated. And that would likely only happen if the cost/risk benefit ratio for getting vaccinated was (perceived to be) unsatisfactory.
In that case, do you really want to criminalize honest, well-intentioned people who are abstaining? I'd say no—that'll create a bitter backlash, because these people don't feel like they deserve to be criminals. Instead, you'd want to educate those people and explain to them why it is worth it to get vaccinated (alternatively, if the vaccine really is too risky, you'd want to improve the vaccine). When honest, well-intentioned citizens oppose something en masse, simply making them all criminals for the common good is likely to make them oppose you, distrust you, and listen even less to what you have to say.