Yep, that is where the rubber meets the road. Walls and national guard troops on the border will have a marginal impact, if the economic incentives remain high. Illegals come here to work, and they work hard, and with no work, they won't come here. That is where the ambivalence comes in. The rap that illegals are coming to America for welfare benefits, is to a large extent, a bum rap.
Regarding economic incentives, the Mexican work force is much more educated and competent and skilled than it was a generation ago, particularly as family size in Mexico drops like a stone, and parents are investing more in the children they do have. Therefore, the value added of these workers in the US has become higher, and thus the economic incentives to come on north have become higher. It isn't about illiterate rural Mexican peasants nearly as much anymore, who are not very effective workers off the strawberry picking fields.
It is something of a tragedy that the Mexcian economy is still so relatively dysfunctional, that the talents of this emerging skilled Mexican working class is not adequately rewarded.
Ya know it is a mystery why Mexico is and always has been a mess politically. Before I retired we opened a large engineering Branch office in Monterrey and we had no problem finding good competent engineers and designers. There are many US based companies in Mexico but It appears that those companies are just using Mexican labor to build and ship the product back into the US. There just doesn't appear to be a "Mexican economy". At least China is building a consumer class along with exports. I really don't get it.