the border thing was probably all about giving government contractors to their friends, particularly the republicans. at least in this case, they are just using government dollars to hook their business associates up.
Fundamental issue is there. There will be people trying to take advantage of any situation.
Of course, Mexicans take jobs from American blacks. This results in increased dependency on social services systems, eg Big Gov, for the Blacks, which Democrats like.
It's relatively easy to "fix the border problem", since it's a false problem created and sustained politically. This is done with false arguments and false solutions.
Require work permits, stop giving citizenship to any newborns, make the work permit cheap but have it include a background check. Toss out the criminal element. Legalize marihuana in the border states, cutting the drug gangs income stream. Determine a somewhat fair set of rules on what social and welfare benefits those with work permits have. Does not have to be totally fair, if that can even be defined.
At that point, it would seem the number trying to go through the desert would be nominal, they'd all go through the border city crossings.
The false arguments are that they should be given citizenship, that employers want their cheap labor, and so forth. The real goal is to pad Democratic voter ranks and therefore win elections. On the Republican side, the goal is to "look Tough on Illegals" to part of their voter base.
To "Fix" this problem, one must look at supply and demand, and influence those factors. I suspect that Rand Paul could get a proposal out that would fix these problems. But I am not certain of that.