"False argument"
You're going to have to back that one up with some details and sources. There's like ten states that have serious limits on collective bargaining. I don't know of any that don't have any public unions at all.
This is the most informative article I could find on the subject, and it implies that it's a lot more complex than "unions/no unions."
For the record, Mississippi's deficit is running about $70 million.