Maybe Twitter will do this and I'm not thinking about it the right way, but here's what I would like to do. I would like to create a text-messaging group so that anyone who signs up on it could send a message to the entire group. Kind of like a text-messaging mailing list.

Well maybe twitter will at some point in the future, and if ever twitter were to catch-on on mass with the general public then you're right that this sort of feature would be necessary.

Anyway, have you checked out http://tatango.com/ ? Basically a group text messaging service.