Before any of those items could come to some fruition, the mob of invaders will be on the border and there will be the choice of letting them in (and the 600 million to follow) or shooting. As for distance to engagement, its relative to what you are trying to accomplish.
Mexico will not stop them, despite half-hearted efforts designed mainly to keep the new trade pact alive while boosting the cash in the police pockets.
As for distance to engagement, its relative to what you are trying to accomplish.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
If Mexico is unable to stop them, use gentle persuasion to allow us to overfly their airspace and have the Air Force run air strike exercises over the horde. Run Bones at 50 feet on full afterburner, I am sure it would get their attention.