what would I do?
bring home 10% of the troops and put them on the border. At that point, the number of illegals is 15 million FLAT, and will begin shrinking slowly.
Some will apply for citizenship. Some will get kicked out as usual. With troops in the area, locals will get more bold with coming fwd with info on coyotes, safehouses, employers of illegals, etc.
I think it wouldn't take a huge legislation move. I think it would be a community effort - hell, we all know a place that employs illegals, or we see people who we know aren't here legally. If the US Army had a base 5 minutes away you could call, and they kept the area free from retaliation, people would rat out the illegals.
That current 15 mil number would also shrink as employers couldn't hire them anymore, and they just went back to mex cause the work dried up.
Guard the border and empower people to come fwd and feel safe as they rat out illegals and illegal employers.