As I read this thread and try formulate an opinion based on the arguments presented by all sides, I think FITZ presents the most persuasive case.
The key to stemming the flow of illegal immigrants from Mexico is to make Mexico an attractive and inviting place to live and work, in my opinion.
I believe that when Reagan proposed NAFTA, the goal was to raise the standard of living in Mexico to a self-sustaining level. "A rising tide floats all boats", if you will. Now if it were up to me, which it's not, I would annex territory in Mexico equal to the percentage of working-age citizens illegally working and living in America, then legalize that percentage. If the Mexican ruling class doesn't wish to provide a opportunities to it's people, we have a dandy system by which hard-working people can succeed.
We don't have much control over that, unless we go with your plan of annexation. It's a bit of an extreme idea. I think we should at least explore the possibility of a fence first. It seems to be working pretty well for the Israelis.