It will work. The leftist open borders lobby will say/find anything to prevent it from going up.
The bleeding hearts like to hearken back to the "good ol' days" of Ellis Island style immigration as a way of guiding modern border policy. Ellis Island was not as rosy as movies and books like to portray....Ellis Island turned away ~2% of immigrants. Note these numbers are of people who actually got on the boat and made the journey. The ocean liner companies knew US immigration rules at the time and most screened all would be immigrants before boarding their ships (the companies had to pay for the return journey for anyone turned away at Ellis Island).
Reasons for getting denied entry ranged from having contagious diseases like TB to holding extreme political beliefs (think crazy anarchists, commies etc).
A porous border with a third world country (yes, it is THIRD WORLD) is not a good recipe for success and has caused among other things crime and disease (resurgence in TB which was thought to be almost eradicated in the US 30 years ago).