That's what a town in Pennsylvania, Hazleton, wants to do. Officials there passed an ordinance that, basically, prohibited illegal immigrants from renting or working in their town. (There would be fines for landlords, and businesses could lose their licenses.) A court declared the ordinance unconstitutional, but an appeal is in the works.
The town argues that their rules don't conflict with federal policy. The ACLU says all hell would break loose if every town got to have varying rules.