Maybe instead of spending so much time and energy on keeping "them" (other human beings) out, we should fix the issue that is causing "them" to so desperately want to come to America (though coming from a poor country to America for a better life has been the way it's gone since this country was founded, and don't tell me every person who came here had the right papers).
One big reason Mexico is so poor is because of NAFTA. We sell U.S. corn in Mexico under "Free Trade" for so cheap that the native Mexicans can't sell their own corn. They can't farm their traditional staple crop and live off of it. They're starving. Oh, and it's our fault.
If you were starving and your family was starving would you wait for papers to save them, or would you risk annoying the people in the rich country just above you? Think about what you would do if you were in "their" shoes.
When people have nothing to lose, fancy laws, papers, and highly-guarded borders aren't going to do a thing, they will still find a way to a better life.
Just like the rest of us did.
By spending all of our efforts on trying to keep "them" out and removal once "they" get in, we waste all of our time and money and energy on a futile effort. As long as Mexico is a miserable place to live and the United States is a better to go, people will find ways in. Instead, wouldn't it benefit everyone if we treated the problem at the source? And then if you want to say "what business is it of ours how Mexico wants to run itself", look around you, it makes itself our business when their people come busting down our door. If we repealed NAFTA instead, and let the Mexicans sell their own corn in their own country, then maybe "they" would stay where "they" belong.