Yes, there is much truth to your assertion.
We took large parts of our nation away from Mexico by force. Now, they are gradually re-occupying their country.
We have made no real efforts to stop this. Every place you call offers Spanish (press 2). Why? Because the businesses that utilize this labor have bribed our leaders to allow this so they can get cheap, hard working labor. Illegal immigration could be stopped cold if all banks, employers, government services etc. were denied without proof of citizenship. This obviously is not being done due to Corporate greed.
Republicans have contributed at least as much, or more, to this situation. So, to then vociferously object is not only disingenuous, it is foolish. Why would you invite someone into your home and then complain about them being in your home? Self-destructive behavior, all in the name of Mammon. If the GOP ever figures this out, they will have a chance to recover.