I've always maintained that a dozen or so two-man teams, armed with Barrett 50 cals, and randomly distributed and moved along the border, would do more to stop illegal immigration in its tracks than (in your example) the Great Wall of China.
Be a whole lot more cost-effective, too. Though, with the price of ammo doing what its doing, there's no telling for how much longer that will be the case. :-)
We could stop it on the other side by buying a couple (or more) Mexican Army Generals.