They'll remain American in name for economic reasons. They know the gravy train would end entirely if they seceded.

Many non-Hispanics would leave. Initially a deluge and then a trickle as even some of the most sympathetic non-Hispanics leave because the "schools went downhill" or there's "too much crime" (they'll never admit their problem is "too many Hispanics"). Plenty of Hispanics would also leave, including some of those who voted for the ruling party and regretted it. Only those non-Hispanics who can't get out for financial reasons, or who are adapting well to becoming "White Hispanics", "Blaxicans", etc. since their old identities like "White American" and "African-American" would be repressed in this society, will stay, a la South Africa, where only poor non-blacks or true believers in the "rainbow nation" remain, and almost everyone else has emigrated.

The Democrats would become an opposition party, with no shot whatsoever at returning to power. Eventually they'd be supplanted by another party as the main opposition. All of the current American parties would not be operating there. Green and Libertarian parties and ideologies have very little popularity in Latin America. The only significant libertarian party, Costa Rica's "Libertarian Movement", for example, is simply a conservative party. "Liberal" parties are always either socialistic (e.g. Honduras' Liberal Party under Zelaya) or conservative (e.g. Colombia's Liberal Party).

The Cartels, especially Sinaloa, would immediately be ramping up operations there. Soon they'd be corrupting the new ruling party's politics, aiming to move their product to the rest of America.

Other ethnonationalisms would benefit in the rest of the US.

Illegal immigration and people smuggling would obviously increase, with it being used as a comparatively easy to enter transit point to enter the rest of America.

English would probably survive for a generation or so to facilitate communication between the races. Eventually Mexican-Spanish would supplant it because the education system would actively promote it over English, ensuring that young people will all have it as their first language.