The French tried that with the Vikings, with predictable results.
Our current immigration system isn't much better. They know if they get set foot on US soil they can request asylum. The courts are so clogged it will be years before they have to appear- and of course they won't. In the meantime they are free to roam about the country, go on the dole, commit crimes, drop anchor babies, whatever. And that's not even including the ISIS members and cartel members who have surely slipped in with them. This is organized at the highest levels and even if not, it is the perfect chance for opportunists.
Good thing we have LRADs. Now would be a good time to use them.
Also, correct me if I'm wrong but I have heard anything close to the border is somewhat of a Constitution-free zone. So maybe Trump can build the wall a few hundred meters back from the border. Whenever anyone enters illegally, they get their distant court date and they get dropped off on the other side of the wall. Still US soil! Hopefully most of them will go home.
Could also declare ANTIFA to be a terrorist group and if any of them so much as flip over a trash can, drop them off in the border zone to give them a lesson in diversity.
p.s. Here are some fresh NPC memes. Already dropped in memes thread.