Ouch. That's what I get for trusting Wiki. But let's roll with the last idea: That the USA grabs most of Mexico due to a failure to negotiate peace with any kind of Mexican Government. What would the USA do with Mexico, now that they've got the whole thing? (perhaps unintentionally)
Trying to hold it would be a big thing for decades, requiring troops from across the nation. Not only does this likely Butterfly a Civil War away by giving the country a different (contentious) focus, but if a Civil War does break out, then the North would have much more experience to take onto the field of combat, as well as pseudo-veteran men to call upon. (On the other hand, Southern military leaders and soldiers are stuck in Mexico with Northern soldiers, while the greater proportion of the North is still freer to fight.)
Some kind of insane reservation system for Mexico? A massive landgrab with ejections of Mexicans from much of the country? Establishment of some kind of Protectorate over unwanted Regions of Mexico?
A reservation system would be impossible, really; Mexico has a massive population, not the relatively small number of tribes that the US did a few at a time. And the US has the almost empty bulk of the normal US to fill, before it can think about displacing and colonizing parts of Mexico. The US just really doesn't have the population, or quite likely even the ability, to drive out the Mexican population.
A protectorate for the unwanted parts of Mexico would simply be called, Mexico. Except for a few parts, most of it wasn't worth it, and was already populated. If we're going for an "all of Mexico" here, it's not going to be by choice.
And, of course, the administration of territory at this point is going to put incredible pressure on the United States. Mexico is going to lose much more territory than OTL, definitely Baja California and much of the Northern Desert. And if the USA is being a jerk, they might take even more and roll the Mexicans right out of that area.
As I mentioned before, the only way to get a most-of-mexico thing going is for the government to collapse, so that no one can sign a treaty while a significant army remains in the Mountains. In that scenario, where anarchy pretty much takes control, there will be no one for the US to negotiate with to make such a deal. The government of Mexico more or less collapsed shortly after the deal OTL; make any deal much worse or extend the time much longer, and collapse it will.
(Oh, and one of the key provisions of the treaty of OTL was that Mexicans in lands annexed by the US wouldn't get kicked out and all that.)
All of this will be happening while US internal tensions are rising...
It really depends on how the political scene turns out, but the Civil War as we know it won't take place. If the escalation of tensions of a unpopular occupation cases the South to secede earlier, it's very possible that it won't be a fight at all, as much as a wave goodbye. If there is violence, a significant part of the lesser Confederate manpower would be in Mexico, while the North would be able to fill ranks faster.