The people who really distrust the vaccine will just think, "Gee, the same government that manipulated everyone into thinking they were all going to die is now

The people who really distrust the vaccine will just think, "Gee, the same government that manipulated everyone into thinking they were all going to die is now manipulating them into thinking they'll win the lottery." This won't convince them, but it might appeal to the sense of greed of the ones who are just lazy and don't like mild side-effects.