I then called the hotel myself, spoke to the guy at the hotel who barely spoke English, but got the same idea across, that we needed to call in the morning. Except I don't work on weekends.
When we tried to convey that this was going to be a problem, an email came back saying the following:
The room request is for Monday, not like it's tomorrow. Not angry at you , but whoever your manager is, this is an unacceptable response. That is why The Law Firm hired The Travel Agency, to take care of the attorneys, whether or not it's last minute, in this case it is not.
Presumably I should be happy there are no strings involved.