There was a debate in congress about whether or not to take all of Mexico after the Mexican War. When the decision was made to only keep what is now the southwest and let Mexico keep pretty much what it has today it was based on the following reasons:
The vast differences between the cultures.
Language barrier.
Corruption and unrest among the population; Mexico had to deal with many revolutions and mini-revolutions, widespread civil unrest.
Widespread poverty among the population.
The main reason it took New Mexico and Arizona so long to become states is because of the same issues, both NM and AZ had to prove to congress they had overcome those problems before being admitted as states.
It seems the politicians then understood what problems could arise if you take on a large population of people who don't basically think the same way you do- it's a shame most don't understand that today.