Our immigration problems stem more from this ridiculous idea that being born here grants citizenship, vs. the parents' citizenship like most other nations. That then entitles the kid to welfare (and by proxy, the family), while they work under the table and pay no income tax...wiring half of their money back to Mexico, vs. spending it here in the US.
Just take away that incentive, and you don't even NEED a wall. That money is better spent on the immigration court system, to determine who should really be allowed to stay (someone productive) vs. a criminal. But, since there really are no harsh penalties for it, many will be deported over and over again, as they keep coming back in.
Of course, we have other nationality immigration issues too. Those from many Asian nations pretty much do the same game. Instead of migrant work though, they pool together and start a business (restaurant, laundry, you name it), and then pay the family working there nothing, as it all goes towards the household. Even darker, sometimes people basically sell their labor to come here, and are basically slaves to the business owner.
All of that though, PALES in comparison to letting in folks who only want to see Americans dead...or who have no inclination to integrate, and demand we bow to THEIR ways. Sorry but Americans just can't comprehend this...and won't stand for it, frankly.