I think Kennedy would be able to suss it out. Finish the wall. Secure the border. When you catch people trying to cross you send them back the way they came. The people who are already here, after we find out who TF they are and make sure they're not terrorists or criminals, can be given the opportunity (not the privilege) to prosper and even become citizens if they work hard.
Discussion
I'm not sure we need much of a wall in the first place. Just cut the free shit. Give a deadline. 2 years and the teat dries up. Stay or go, your choice, but no taxpayer-funded handouts or healthcare, and no American Constitutional rights. You're not an American citizen. Make no mistake, some will ignore the warning and it will go poorly. Far less than the profiling and human round-up that it would take if you leave the incentive to stay in place. Anyone thinking I'm an ogre for putting it that way needs to spend time in STX to gain some perspective. The current system is a crap deal on all sides.