Let me ask because I do not know. Aren’t the National Guard under each state’s governors and not the president?
U.S. Const. art. I, § 10 No State shall, without the Consent of Congress, lay any Duty of Tonnage, keep Troops, or Ships of War in time of Peace, enter into any Agreement or Compact with another State, or with a foreign Power, or engage in War, unless actually invaded, or in such imminent Danger as will not admit of delay.
U.S. Const. amend. X The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
All States retain the right to self defense. The Federal government has refused to provide for the common defense, the raison d'etre for the Federal government. The States must repel invasion or the people will.
Texas
The Texas Governor has the authority to call forth the state military forces and the reserve militia to repel the invasion.
Tex. Gov. Code Sec. 431.071
http://www.statutes.legis.state.tx.us/Docs/GV/htm/GV.431.htm#431.071
Tex. Gov. Code Sec. 431.001
http://www.statutes.legis.state.tx.us/Docs/GV/htm/GV.431.htm#431.001
Tex. Const. art. 4, § 7
http://www.statutes.legis.state.tx.us/Docs/CN/htm/CN.4.htm#4.7
Arizona
The Arizona Governor has the authority to proclaim an emergency and mobilize all or any part of the state guard or the unorganized militia into service of the state.
Ariz. Const. art. 5, § 3
http://www.azleg.gov/FormatDocument.asp?inDoc=/const/5/3.htm
Ariz. Rev. Stat. § 26-174.
http://www.azleg.state.az.us/FormatDocument.asp?inDoc=/ars/26/00174.htm&Title=26&DocType=ARS
Ariz. Rev. Stat. § 26-122.
http://www.azleg.state.az.us/FormatDocument.asp?inDoc=/ars/26/00122.htm&Title=26&DocType=ARS
Ariz. Rev. Stat. § 26-121.
http://www.azleg.state.az.us/FormatDocument.asp?inDoc=/ars/26/00121.htm&Title=26&DocType=ARS
Ariz. Rev. Stat. § 26-172.
http://www.azleg.state.az.us/FormatDocument.asp?inDoc=/ars/26/00172.htm&Title=26&DocType=ARS
N.B. Unlike Arizona SB-1070, these do not pertain to immigration but to a proclamation of an emergency and the protection of lives or property.