The fact that Christians generally don't like to vote (which I wasn't aware of until just now) is relevant to the question of why he said "we'll fix it so good, you won't have to vote".
Christians do vote and see voting as a way to push for the legal restrictions they want. Them not having to vote anymore, because the rest of us cant get abortion, anticonception whatever else allowed through political process anymore is literally definition of "going away with democracy".
Which is actual political goal of radical evangelical christians, if you actually read what they write and listen what they say. It is not about them being allowed to be lazy, it is about them successfully creating religious state.
