There is a long tradition since the end of reconstruction that the Military is not used to police citizens. this was part of a political agreement that led to the Southern States being re-admitted to the Union. Th southern States didn't want the military coming back in to a state and taking over government again.
So the military not doing police work has a strong element in the conservative principle of "states rights"
I think you're talking about the Posse Comitatus Act. It's another area, like born citizenship, that will have to be worked out in the courts. I do believe that if the situation reaches the point of a mass of people trying to overwhelm the border, Pres Trump will have them prevent it and then we'll see what the courts have to say. It's going to get complicated.
I think there should be a constitutional amendment clarifying all of the citizenship issues
certainly a debate worth having
For now. It can always be ordered when needed, and right now would only give the idiots something to whine about.