A well crafted shodan.io search given the already public information (approximate size, in the US, no password, etc.) should give you a good start. It's already been found once.
I'm not sure how to search by database size though. But I'd estimate that 190 million voter records, at 1 kb each, would be a little under 2 GB if my math is right.
I'm not familiar with MongoDB and don't have the time to learn right now. But do check it out!
Confirmed: db.blackhole_nj.find({$and:[{"fname": "Christopher"},{"mname": "J"},{"lname": "Christie"}]})
The governor's DOB in the results matches what's in Wikipedia.