I decided against an emergency plumber. I got up there last night and cut a hole in the drywall to see if anything major was lurking underneath. It was (as expected) damp, but there was no standing water or anything, so I let it go overnight. I marked the area with a pencil, and the spot hasn't grown, which is good.
I'm glad I waited. I have a guy who can do this type of stuff, but he's not an emergency-type resource, so I couldn't call him until this morning. When we talked, he said he doesn't think it's going to be a big deal, so I'm hopeful I won't take too huge a hit with the bill.