Update

So they claim to have received 4 offers. They're going to sleep on them and decide what to do tomorrow. They indicated they may counter, but one of the offers was significantly for more than ours.

They say.

I dunno if I believe them. I'm not really set on this place, as much as I like it, so I'm going to wait and see. If they really have a better offer, that's ok, they can take it; I'd rather lose the place than let them play hardball.