From my understanding, ther would have to be a pretty massive change in politics in Washington D.C. for this to happen. I know there was a small "take all of it" group, but the benefits didn't outweigh the risks. Integrating a sparsely populated region that your people are already settling anyways is one thing, but annexing a heavily populated country with its own language (different from your own), its own religion (different from a lot of your people) and own traditions (not your own) is very different.
Now, this being ALTERNATE history, why not? I can see some debate in Congress about the relative slave/free state status of Mexico proper, just as there was about the OTL Mexican territory taken. Did Mexico have slaves at the time in any way? What was the attitude of the Mexican elites regarding slavery?
The occupation of Mexico could be difficult if there was guerilla resistance. And considering that Mexicans often waged guerilla war against Mexico City governments, I see no reason why they wouldn't aginst a Washington government.
So assuming a Civil War-like conflict comes about, I can see Mexico breaking away as well. This would leave the Northern leadership with a quandry: fight to keep the South or fight to keep Mexico? I imagine that the Northern leadership would be willing to come to an agreement with Mexican rebels as opposed to Confederate ones, since Mexico would be such a recent addition.
Against all odds, if the US was able to hold on to Mexico following the annexation and a civil-war like conflict, I can see some fairly major changes in the US. Maybe we would actually have two official languages like Canada as as opposed to a de facto official language. The post-Civil War "Wild West" era would probably be far different. I wonder how the larger population centers of central and southern Mexico would effect Western expansion? With that huge empire, there may very well be no reason to pick a fight with Spain, so the status of Cuba, Puerto Rico and the Phillippenes would be different. No Zimmerman Telegram, assuming there is still a similar WW1, and the US might still be busy with the Mexican Insurrection in the early 20th anyways. It would be kind of cool to see Pancho Villa leading a Mexican Revolution against the US occupation.
Would the existing Mexican states be admitted as states to the US? If so, with what criteria and in what order?
EDIT: Basically what I'm saying is that its a cool idea and rife with butterflies, but I'm not sure what a good POD would be. Maybe, somehow, the US sees itself as imperial (Manifest Destiny and all that) in a slightly different way. Like, say, the US actually conquers most or all of Canada, and Manifest Destiny then comes to mean the US including all of North America?