Annexing all of Mexico means having to incorporate a massive population (In the millions) that hates the "occupiers" with a massive vengeance. The topography of southern Mexico is really mountainous and tropic and guerrilla warfare would be a nightmare. It would cost many American lives and would cost a pretty penny to fight a conflict where gains would be slow (and morale would likely be low) and the opposition will never quit until the occupiers are removed. The closest thing to annexation that could ever happen would be to chop up Mexico into a series of satellites: Chiapas, Yucatan, Rio Grande, Veracruz, etc.
Also I'm pretty sure the US has never claimed to have a unified language, and has never proclaimed itself of having a white character. Citizens of the nation may have, but not the state itself.
Also the US does accommodate states according to their needs. Louisiana and Florida used to be French and Spanish language dominated states. Louisiana doesn't have counties, but parishes. New Mexico has a bilingual state constitution, and was founded as a state mainly for the purpose of being a state specifically for the annexed Mexican population. Utah is a state specifically for one religious group, and Indian reservations have been around since 1851.
There was a move to hold a referendum on the very subject of American Annexation in 1991 when a US Senator visited.
http://en.wikipedia.org/wiki/51st_state#Albania