Texas and Florida can just stop accepting any Illinois driver’s license.
I think the problem is that the "full faith and credit" clause of Article IV requires them to accept it.
Article IV Section 1Granting a state driver's license is a "public act" and the license itself is a state "record" that must be given "full faith" in all the other states.Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.
States must appeal this to the Supreme Court on the grounds that some states are forcing other states to accept their decisions on illegal immigrant status and that should be the purview of Congress, not individual states, to legislate.
-PJ