Some alternate histories have dealt with the US annexation of Mexico following the end of the Mexican-American War (1846-1848). By the end of the war the United States held Mexico City and had severely weakened the Mexican army. It would appear that the US was on the verge of annexing Mexico, but instead in OTL they settled for what would become known as the Mexican Cession.
Many who believe that the US annexing Mexico was probable point toward the military victories of the US and the support of the expansionist "Young Americans." They ignore the large loss of life to the American forces with over 13,000 dead and only 1700 by combat. Mexico also had a culture vastly different than the current culture of the United States, making administering the area difficult.
Its possible that an earlier POD might have made an US annexation of Mexico more likely but to have one happed after the Mexican-American War is unlikely.