Governors cannot unilaterally call up the National Guard for reasons associated with an exigency beyond state borders. Likewise, were a governor do so and was overruled by the President (whose authority has higher standing) significant
embarrassment (or something like it) would surely follow.
Perry can also refuse the Presidents authority.
We have a crisis and the President is not acting in the interests of the U.S.
The stand off would obviously create a constitutional crisis, but Perry has the support of the American people
The President cannot unilaterally do half the crap Obama's doing either. Play that game, make them stop you from defending your borders.
Easier to ask forgiveness than permission.