The liquid nails is a great adheasive, but I've seen it take up to 10 days to set, at least when I do laminate counter tops that is :lol
I had the same thing happen recently too, the best way IMO is using support rods in combination with an adheasive, as someone else mentioned. If the the adheasie gives without the support of the rods, you get a sculpture "face plant". The rods will ensure that it at least stays in place.
Not sure about the goop though. I've seen goop melt down expanding insulation foam. Not sure what it will do to urethane foam. Whichever these busts are made of. I used a industry glue I got from a job, it's like a clear silicone caulk, but fast setting. Also used for countertops. Unfortunately there isn't a name on the bottle :lol
stay away from air-dry glues, and use a 2 part epoxy, or even Bondo. Bondo ought to work fine, as it it thick enough to smoosh into the foam and lock into th e"bubble texture" on both halves of the piece. It will cure in minutes and you have a armature again.
I second the 2part epoxy. It's the only glue that I've never had react to anything that I'm trying to glue together. Definately use the rods as well, it'll add more strangth overall to the head so the next time it hopefully won't come apart on you again... well at least it definately won't in the spot you epoxy'd, hehehe.