RadioLab did a phenomenal series on illegal immigration years ago. One thing that stuck out to me and has stayed with me ever since was an interview they did with a woman who had been deported multiple times, risked her life multiple times, denied a visa and asylum multiple times. They asked her why she kept trying to get across the border and she said that the alternative was death for her and her family.

Whether or not she was being honest I don't know. But it did make me realize that the broken system has created an all-or-nothing choice for so many people. No punishment or policy could ever outweigh the alternative for them, so you'll never be able to stop immigration, illegal or not.

I'm sure I'm not doing the argument justice, but your comment reminded me of it.