Doesn't Huckabee support teaching creationism? I'd be surprised if the teacher's unions would get into bed with someone with such views (or with even the most big-government republican over any mainstream democrat really).
The dude actually
raised taxes in Arkansas to spend more money on "education" (which is, in the end, what the teachers' unions care about the most). Meanwhile, Obama has seriously pissed off the teachers' unions with his whole "Race to the Top" thing, so it's not a terribly unlikely scenario. It's probably not the most likely even if Huck were the nominee, but it's not implausible.