The federal government is not dependent on state consent to protect them from invasion.
National defense is a constitutional responsibility of the federal government and it has the duty to enforce the federal laws.
The Constitution is the supreme law of the land and state officials feelings about it are irrelevant.
Our border will be secured.
Conversely, states are not dependent of federal consent to protect themselves from invasion.
Article I Section 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.
If Nevada Gov. Brian Sandoval's belief were true that deploying members to the border would be “an appropriate use” of the of the National Guard, there wouldn't have been a need for this clause in the Constitution.
States can act unilaterally to call up their own state guards to defend their own borders, citing "imminent Danger as will not admit of delay" to bypass Congress. Since this so-called caravan is planning to enter via Baja California, it is unlikely the Jerry Brown will call up California's guard, but other states bordering Mexico certainly can.
Put the troops on the Arizona and Texas borders with Mexico, and wait for California to cry "Uncle" as the invading hoards overrun their state as the only avenue in.
Beef up the border patrol and/or state guards on the California-Nevada and California-Arizona borders to catch those who make it through.
-PJ