I put this as a response to one of the comments - probably the wrong place. Sorry about that.
I think the only ultimate solution to the US "immigration problem" is to work to remove the border, period.
The Europeans did it, although it took them 50 years. If Germany and France and Italy can drop their borders after hundreds of years of war and mistrust, we can surely do it with our neighbors to the South.
Europe had a bit more of a running start, as their economic differences were not that great. But they have continued the effort with the Eastern block, where the problems are major. This is not without problems, to be sure - but it is moving forward.
The people who come here, legally or illegally, do not come for our climate, or our scenery, or our language and culture. They come for the economic opportunity. They have energy and initiative, and are willing to take a risk, as much as my grandparents did when they left Germany in 1880. If their world gave them the basics required for that opportunity, they would show that same energy there.
To drop that border, we need to help Mexico invest in its own infrastructure, to provide the education, the stable infrastructure that fosters our economic entrepreneurship. Ultimately, it will be cheaper than any wall, and the economic benefits will be huge for both sides.
This is not an aid program, not a giveaway, this is an investment to create a mature trading partner of equal stature.
What would our world look like if any one of us, or any one in Mexico, could walk across the border, apply for work, earn benefits, attend school, pay taxes, etc.?
We might actually be on our way to becoming a full citizen of our own hemisphere - and eventually the world.
Let's call it a "reverse domino" theory - knocking down borders by spreading economic opportunity.
This will not be accomplished by some phony indoctrination in the "American Way". What is needed are the simple basic opportunities described by Amartya Sen in his book, Development as Freedom. If humans are given the freedom to do so, they will prosper. All they need is the opportunity.