For arguments sake, lets assume the LA purchase has gone as OTL, and now a war with Spain has popped up. OTL, there was a squabble over where the border is (and even whether the purchase was legitimate from Spain POV). If there's a war, it's only natural that US is going to push a greedy claim. My opinion is that the purchase is what really put wind in the sail of manifest destiny, and even though it's not in full swing yet, manifest destiny, and greed will be factors.
The big bugaboo is that US doesn't have much ability to project power that far. They'll want to, though. Don't know how big a separatist movement there is in Texas at the time, but US will back it if they're at war. I believe they had just stolen west florida that way (hey, there might be a spark for the war)