This.
Contrary to the popular misconception, DL's are NOT required to be recognized by other states. Driver's license reciprocity between states does not involve the federal government. States enter into a compact between themselves to recognize one another's driver's licenses, and in some cases even agree to report infractions to one another.
There is no federal Constitutional justification for forced reciprocity of firearms licenses. Technically, there's no federal Constitutional justification of firearms licenses, either. To support forced reciprocity is to support further erosion of the United States Constitution.
Senator Cornyn is joining the NRA in misleading uninformed gun owners to further an anti-Constitutional cause.
This^