My wife and I filed jointly. She is a Florida resident and I am an Illinois resident. Illinois wants both of us to file? How when she never worked or lived there?

Illinois does allow a married couple to file separately for the Illinois state return regardless of how they file their federal return. The process in not easy when using TurboTax software. 

HERE is a TurboTax link explaining how it's done using TurboTax. 

Basically you need to make a mock federal return in TurboTax for you as single, then the Illinois return will only pick up your information and compute a Married Filing Separately State return.

Disregard the mock federal once the state is done. 

You won't need to make a second mock federal report since there won't be  a need for a return for Florida.