Divert funds currently earmarked for foreign aid to provide free cell phones to all of our Mexican "friends." Make sure we have a network of cell towers on the US side of the border, and along the Gulf coastline, that are robust enough to send and receive signals quite a few miles into Mexican territory and the Gulf. Re-task some N$A resources that have been used to track US citizens to track all of our Mexican "friends" who move within range of the robust cell tower network. Make the cell phone gift to Canada as well, as a North American initiative, to deflect suspicion. Promoting the North American cyber economy, or whatever.
You know the demographics of the likely illegal immigrants will make many of them Facebook users, so persuade Mark Zuckerberg to pony up part of the upfront costs. Maybe throw in a few bucks from the guy who gets "Angry Birds" royalties.
That's gotta cost the American taxpayers, net, less than an actual wall, and unlike a wall, lets you track the incoming horde in real time. Let each state figure out how to deal with the illegal immigrants once they've been located IF they try to illegally enter the US.
Make sure that adverse consequences suffered by those who are "located" are widely publicized in Mexico. Heck, you could even use the very same cell phones for that purpose, as long as such publicity was included (i.e., hidden) in a flow of other information. Keep our "friends" in the dark about how they were located by creating a plausible cover story. If we could fool the German war machine in WWII about our breaking of Enigma coded messages, we certainly ought to be able to fool unorganized immigrants. Let a few cell phone packin' friends get in, just to further hide what's really happening (just like some Enigma-based intelligence was not used in order to protect the secrecy of the successful Enigma code breaking).
We put a man on the moon in a decade. We can get this done.
Next problem?