I'm thinking that even a veto isn't going to do it.
Pro-active means are required.
It's time for Mr. Trump to declare a "national security emergency" to exist along the entire length of the border, and through that acquire the funding with which the military can begin border reinforcement, including construction of a physical barrier. Such funding can probably be squeezed out of existing military appropriations, which won't be subject to Congressional approval.
That's probably the only way it's gonna get done.