For those asking. The President has complete authority under the Constitution of the United States (Title 8 U.S. Code § 1182) to stop the migrant horde currently on the way to the border.

Article 4 Section 4 of the Constitution also grants him the power.

Section 4 – 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.

h/t GenericInsult