It's amazing how much resistance there is to this idea. Apparently, many of the "close the borders NOW" folks are perfectly content to leave a bunch of soldiers out in the desert Southwest with little supervision, lots of temptation, and little clear mission. They don't want to have the military do what it CAN do effectively; they prefer it to do what it's manifestly NOT intended to do and leave the problems that drive illegal immigration in place and unsolved.
They want to stick a band-aid on a cancerous lesion.