Three union organizers have handed out fliers to employees outside the jail, asking the workers to sign and mail in authorization cards.
Some employees say they're forced to work 16 hour days and that some have worked 19 consecutive days without a day off.
Warden Jim Cooke says reducing overtime is his top priority. Cooke also says he doesn't like the idea of a union at the privately run jail.
The jail is operated by Tennessee-based Corrections Corporation of America.