America's decision to leave the safety of Veracruz and proceed towards Mexico City proves to be costly. With their supply lines cut off, and receiving no help from Washington, Santa Ann'as Mexico is able to effectively end the existence of an American army in Mexico by waiting it out. Santa Anna sees an opportunity to strike hard against the American dogs.
What would have happened if Santa Anna had defeated the USA and created a dictatorial empire more powerful than the United States?
Mexico receives Texas in the peace treaty. Soon, the Civil War is upon the United States. Mexico is advantageous and strikes hard first against the Union. The CSA do not officially recongize an alliance with Mexico, and are cautious of Mexico's real ambitions. The CSA wins the war, achieving their Independence. Soon, both the USA and the CSA see that their are vulnerable to a Mexican attack. The USA and the CSA agree to form a defensive pact, promising that if Mexico attacks either one, they will intiate a responsive operation against Mexico.
Mexico tries to create allaince with the USA but it fails, and Britain also declines an alliance b/c they like seeing an American divided between three nations, and have no desire to support a large American Empire. With no allies, Mexico declares war on the CSA, and thereby declaring war on the USA as well. The USA and CSA are able to produce too much industrial power towards the war effort and soon the egotistic Santa Anna finds himself once again, inside the walls of Mexico City, trying to rally forth his men against an American army. However, Mexico City falls, and Santa Anna with it. The CSA and the USA split Texas and establish a friendly democratic government.
However, an increased Catholic presence in Texas, due to Mexican occupation, creates dissent towards what the Texans see as infidels and foreign. Soon Texas revolts and have Mexico, the CSA, and the USA breathing down their necks. But a foreign influence decides they want to further divide America, Great Britain. Soon the USA and CSA back down, recognizing Texan independence.
Further down the line, their is no American involvement in WWI or WWII due to the lack of any means to effectively carry out operations against the German Reichs. However, in both wars, Germany still falls, but Japan creates an Oceanic Empire and becomes the leading power in the East.