The US Constitution provides explicit and unambiguous authority AND the responsibility to protect States against insurrection and invasion. It's not really debatable that an invasion is occurring at the border with Mexico. A truly Constitutionalist executive (POTUS) would simply tell the legislature and judicial branches to fuck off and take appropriate Constitutional measures by whatever means are at his disposal.
In fact, POTUS was calling the border "caravans" an "invasion" for weeks on end. (Anyone else recall his presser disagreement with Acosta over "invasion"?)
Article IV, Section 4 of the U.S. Constitution
"The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence."