I phoned the vet who's on call today — it turns out he's the one who took care of Collette between 2003 and 2006 — and he told me to bring Callie in immediately. I did. He took an x-ray and said he could see that Callie has swallowed something that has blocked up her digestive system. It could be a little rock, or a little green apple (the yard is full of them), or a cork or other piece of wood.
The upshot is that she is having emergency surgery this afternoon. The vet will call later to let us know how she comes through. And then, if all goes well, we'll be able to bring her home tomorrow during the day.
It's always something, isn't it? Keep your fingers crossed.