A story in today’s St. Petersburg Times about a Department of Labor investigating the failure of a state agency to pay proper overtime, mentions lawsuits against the Department of Children and Families under the Fair Labor Standards Act.
While the federal government can sue states for violation of the FLSA, the Supreme Court has held that there is no private right of action against the state. See Alden v. Maine.
So at least right now, the employees are likely to lose their case, unless they can get the Department of Labor to take their case or there is a change in how the Supreme Court views these cases.