I've just done some light investigation, primarily using MIT's living wage calculator. As it happens, the state with the lowest living wage is South Dakota. For one adult with no children, the living wage is $15.15. If you want population replacement to work out, then you need to pay enough for two adults with three kids to afford to live while only one adult is working, so minimum wage in SD would need to be $40.02. The minimum wage in South Dakota is $7.25.
What. The. Fuck.
As a sidenote, there's no federal definition for a full-time vs part-time employee. Because of this, you could work 50+ hours in a week and still not receive the benefits of being a full-time employee.