The externalities of not getting vaccinated (see: this article) makes a strong case for requiring them or at least making a subset of them required upon exit for reentry (similar to passports) without religious exemptions.
Do you want a country that prohibits people from leaving when they want? So you can't require it on exit.
And the most basic right of citizenship is the ability to enter the country, so you can't require it on entry either.
All you can do is convince other countries to prohibit entry without vaccination,
http://www.cdc.gov/ncezid/dgmq/feature-stories/welcoming-new...
That said, American border guards have been known to turn back drunks coming in from Tijuana, but mostly as a favor to them (since they'd need to be arrested upon reentry due to public drunkenness). If you were in such a situation and insisted upon your admittance, however, I believe you would be let in.
I think it was a good idea. Too bad there's no vaccine against bot flies :(