Well, Poe is spending the night at the animal hospital. He was dehydrated when I took him in, and wasn't eating. The vet is giving him IV fluids, and said he's already eaten a little and is keeping it down. She's going to keep an eye on him, give him more food to build his strength up, and hopefully he'll be back home tomorrow afternoon.
We aren't sure what the cause of all this, but I have my suspicions: dried basil. I found...let's call it evidence...that Poe had decided to spice up his life and eat some dried basil, stem and all. We think the stem might have been agitating his stomach until he was able to get it back out, but by then he was already getting dehydrated and didn't want to eat because he kept getting sick.
So! Lesson learned. The basil is going in the trash. We hope that's all it was.
Thanks, Cima, for pointing out the dangers of possums, and so sorry to hear about the run-in your kitty had with one. We'll definitely keep an eye out for this big one.
And thanks to everyone for your well-wishes for Poe. I'm sure he's feeling better already. :)