Elfdart wrote:
Someone smarter and less arrogant than Santa Anna might have pulled off what you describe, but such a person wasn't in charge.
Indeed, Santa Anna was extremely lacking in military and political skills. Had a competent general been in charge, it might have gone otherwise. However, that pretty much would have needed a whole different historical backdrop, starting a few decades earlier, perhaps even more, down to the
esprit of Mexico. Meaning: had Mexico not been torn apart by internecine war lasting for decades under no stable, lasting government; had the not been selfish and guided by political gain (some Mexican generals didn't even provide backup or relief forces for other Mexican generals of rivalling factions in actual combat), it would have gone quite differently, As Mexico's own Luis González de Alba eloquently puts it: "historians told us that this was a war fought between the big and the small. That much is true, but actually, it was a small yet belligerant and determined David, against the southern Goliath, big and clumsy, Catholic and prayer-prone. The former relying on gun production, the latter on the Virgin of Guadalupe".
So, in such conditions, and just looking at the sheer potential manpower, resources and territory, it would have been quite feasible for the Mexican army not only to win that one war, but to march all the way to Washington and occupy it, had they deemed it necessary (to address the OP, in a way, because Santa Anna should be out of the question for this to work).
Nevertheless, as I mentioned before (and as with all Alternate History should bear in mind), it would have required Mexico to be very different in its very essence, as things that happen in history are direct effect of their causes -things that happen before that, which in turn are brought about by the other things that happen before them, inexorably. So, as some say, things happen the only way they can.
Nowadays, though, with Mexico ranking 12th in territory (nominal, National Geographic states that it's so mountanious that if its total surface were to be flattened it would cover all of Asia) and 12th at GDP (purchasing power parity) as of January 1st, 2008 according to the CIA World Factbook, I think such preocupations aren't significantly hindering said country's development.