That's the idea. And the reason people here illegally should be deported. Period.
Political power in the U.S. is based on votes. So...just get enough of your people into the country, keep them unassimilated by keeping their language, customs, and loyalties, and pretty soon...bango. You own the joint.
All it takes is a weak country run by spineless politicos who worry only about marketing themselves to the "electorate". The Mexican leadership has sized up American "leaders" and pretty much come to the conclusion that they can made to sit up and bark. Or whimper, to be more precise.