Say you had a problem with bugs in your kitchen. You had a big pile of spilled sugar in the middle of the kitchen floor, and it just kept attracting bugs. You complain to me that you've tried everything: roach motels, bait traps, hermetically sealing your house, but all to no avail since the sugar keeps attracting bugs.
I'm just going to stand there and blink in goggle-eyed amazement, wondering "Why don't you try getting rid of the sugar in the middle of the floor?"
There is always going to be a problem when a prosperous nation has a land border with a poor one (you'll note that we don't have swarms of Canucks pouring across the border, except maybe to buy cigarettes,) but why compound it by offering a vast cornucopia of free stuff that makes entry too enticing to resist? As long as this is the land of the handout, people who want handouts will come here looking for one. When you subsidize freeloading you can't complain about freeloaders, domestic or imported.