"a surge of "extra-continental" migrants from countries far beyond Mexico and Central America, and how the nation will head it off."
One blocks off a "surge" of humans similarly to how we might block off a surge of water:
With a physical barrier sufficiently strong enough to withstand the surge.
That's what the full-length border wall is all about.
I'd go so far as to suggest that we might consider closing the manned "points of entry" at the southern border, as well -- ALL of them.
No one going either way.
For travel between Mexico and the USA, it can be by boat, or plane.
Both of those are much more easily policed.
Sooner or later, we may have to start thinking about a physical barrier with Canada, as well.