Turbotax keeps checking that my spouse is claimed as a dependent on my state return. When I fix this error it still does not allow me to e-file my return.

I would check in the My Info section of TurboTax to verify that your spouse's information is correct. When you click Edit next to their name, you will be taken to their entry screen, and section #3 asks if they can be claimed as a dependent on another person's return. (see screenshot)