First, I doubt Cain actually meant citizenship — he just says things without thinking, and without understanding what he means until later.
Still locals or states, you can’t have people’s legal residence in the country decided on a piece-meal basis by extra-legal panels. Gingrich’s plan is absurd — you can’t tell an illegal they are deported in one town, and can work in another town. And you can’t have each state deciding whether an immigrant is allowed to work in the state or not.
Either the immigrant is legal or illegal. If they are illegal, they need to be deported, we can’t have sanctuary states like Cain seems to be setting up. If they are legal, you can’t discriminate against them on a state-by-state basis, treating them as 2nd-class citizens because legal residents are protected by the 14th amendment.
So are illegal residents. Search "Yick Wo" (versus, I forget whom).