Walls and fences are effective only if there are men guarding them, this is a concept that was well developed even before the bronze age.
I think what might be more effective is a drone surveillance system across the border, identifying trespassers, and a rapid drone response team that can track them and warn them to go back after they cross. The border patrol can then simply be a rapid reaction force to confront those who ignore the warnings.
I'm not entirely opposed to some sort of fence, but there's no need for an expensive, tall, sturdy wall. The fence can do the job that most fences in people's yards do, which is to delineate the boundary rather than deter intruders.
Personally I think this issue is being overly politicized like just about everything else. I think most reasonable people would agree that control of the border is a good thing. I think some sort of barrier over the border is also something that can be reasonably debated. It's too bad that just talking about it evokes so much emotion on both sides that you can't debate the pros and cons without being labeled something derogatory by the opposing side.