After posting this, and responding to a few threads, I wasn't able to be online again until right now. I've taught that class again, and here's the update. I got an amazing response from everyone on campus -- the provost, the head of campus police and even had a plain clothes police officer in class today. The "threat" was taken very seriously by the campus powers that be.
A student security escort actually is in my class as a student (didn't know this before but found this out from the police officer) who HAPPENED to be sitting right in view of the student who made the threat on Tuesday. The student security worker was interviewed by the police officer and our versions of what happened Tuesday are identifical so it was "verified" today by the police. Always good to have that verification. We're working on identifying the problem student. No incidents at all today though. I wasn't able to recognize who it was (it's a large class). Hopefully it's just someone being a jackass. But after our history of having had a gunman on campus shooting student victims, and right after Tuscon's tragedy (!!!!) for someone to make these comments is just nuts.
I appreciate ALL of the comments. They were all helpful in various ways. So THANK YOU ALL. I will be able to even use some of them as potential suggestions with Admin and Security/Police (just one example: Leo's suggestion of the availability of photos which we at present don't have). You've been a very helpful bunch. I appreciate this a lot. I was a bit stressed by it all but feel much better now.