If your read California history, the "Americanos" lived peacefully and lawfully with the Spanish government based in Monterey until gold was found by the settlers in 1849.. The Spanish governor used his army to try to take the legal claim away from the settlers. The settlers fought back an won. It was the settlers that caused the Spanish governor and the army to concede the territory and withdraw back to Mexico, not the US..
As for the second part of your "signature". "A constant flow of people over the border can lead to an invading army in time." You sure pegged that one. What we have is an invading army, not immigration or integration..
The whole idea behind immigration is to welcome new people and give then the opportunity to bring themselves up to our standards, not bring ourselves down to theirs.
For almost 200 years (we can forget the past 40) the US had been a shining example of the benefits of democracy and free enterprise. We don't have to live in Mexico City or even take a short stroll across the border into Tijuana to see what this "invading army" has brought to our cities..
By any definition of the word, Opportunity, doesn't mean a guarantee given under the tax payer's dime.
Nor does integration mean we have to adopt their language, customs and lower standards of living.
There is a huge difference between immigration and colonization.. The colonial period is dead..
Sure, The US has experienced many waves of immigration in our history, but after a generation most of the problems disappeared and they were proud to call themselves Americans. They integrated into our culture, language and way of life, and shared their language and culture with us.
Is this "invading army" so inferior they can't do the same thing??