There are about 100 million people in Mexico and even their most conservative politicians are socialists by our standards. That many people would entitle them to 1/4th of the seats in Congress. The number of Senate seats and Presidential Electoral College Seats would be determined by the number of states that we broke them into.
With 100 million new poor people mostly voting for Democrats, do you think there is any chance that Republicans would ever control Congress or the Presidency again? Do you think these people would be voting to rollback welfare and socialism? I doubt it.
Just the cost of enrolling them on our current social programs would break us. The vast majority would qualify for the Earned Income Tax Credit which is welfare disguised as a tax refund, foodstamps, housing assistance, and on and on. And then we would get to sign up all these people up on social security.
It is a horrible idea that would drag the USA into the third world!
If Mexico were to become a state, yes... If we were to annex them like Puerto Rico, Guam and the Virgin Islands then no... They do not have voting rights nor are they in our welfare system.