I have to wonder myself, if a intergovernmental military body comprised of our enemies were trying to pull Mexico into their pact and potentially put troops right on our border, or say block off a major food source to America what would we do?
Fist, you'd be assuming the Mexican Government is in charge there. They are not. The drug cartels are in charge.
Second, the cartels would have to agree to having a foreign country move into an area the drug suppliers need open to move their product. They would need to be allowed free passage, or there would be a fight to keep them out.
Third, the flow of illegals would have to stop, because the new "neighbors" would not be able to tolerate the lack of security that situation brings.
Lastly, the Mexican Government would have to be prepared for the US backlash should they allow the stationing of military weapons. That alone would make Mexico and the US adversaries, something I believe the Mexican government would try to avoid. Their new "friends" would have to be able to promise them at least as much as what they get from the US without even addressing what the Cartels would be losing.
Look at what the sanctions against Cuba has done to that country over a few decades. Mexico would be in an even worse position due to the shared border with us.