The wall will make it more difficult to enter the USA. See how few managed to pass the intra-German border when the wall was up. That can be achieved in the USA too, probably with even better results due to modern technology.
Its a little easier to deter people when you use land mines and shoot on site, particularly when you give your border guards a bonus for a kill. Is that what you propose?
Also 'the wall' would be on much more hostile and remote terrain and be much longer than the inter German border.
Land mines and shoot to kill, tactics used to keep invaders out. Tactics used by communist nations to keep their imprisoned populations in. Tactics that European communist nations dispensed with during the last 15 years of their existence, though China may still use them and NoRK definitely does.
The Inner German Border and the Berlin Wall was right at half as long as the border between the US and Mexico. The population of East Germany was about 5% of the US population, so it would seem on that basis alone a border wall with Mexico would be far cheaper for the US than was the Iron Curtain for East Germany. It was a bit better for Czechoslovakia as their border; fenced, walled, and guarded was about 1/4 that of the US Mexico border with a population of just less than 5% of the US.
For all the hand wringing there weren't all that many casualties. A few people killed trying to escape tyranny in the early days worked well to dissuade others from following. So I should think that should a few invaders lose their lives, followers might similarly be dissuaded.