The biggest thing building a wall will accomplish is to keep illegals who are already here, in the country. Not out. I used to know people who would come work (illegally) in ag or restaurants, or other menial work, stay for a year or two, go back home for 6 months, come back and work for a year... etc. Putting up a wall would prevent them from returning to their families when they have money to survive. So then what is the choice? Never see their families again? Or try to smuggle them into the country too?
There was an interesting segment on NPR a few days ago about this. I'll see if I can find it.
I was listening to an economist discussing the Farm Bill, which is up for re-working again this year. The Farm Bill subsidizes crops like corn and soy, which can then be bought below production costs by junk food companies, (and other food companies.) The point was made (besides obvious correlation to cheap crappy food, and obesity,) that this has had severe impact on the global economy. Since these crops can be trade staples of other parts of the world, but the US subsidizes the giant crops so heavily, it has reduced agricultural economy in many nations, including our own. Small sustainable farms (many of whom provide employment for migrant workers,) are either going under, or converting to corn-syrup crops. Shame really.
Anyways, the point is that if the Farm Bill is fixed, subsidies like this are redistributed to sustainability, it changes the quality and availability of good food, AND it provides a boost to other countries with agricultural economies... which gives them jobs at home... which reduces illegal immigration.
Building a wall is a band-aid.