Welcome to my 2nd USA game, after the AAR, gentlemen.
The release version is a much tougher opponent than the version I was playing my AAR with. You're going to have to play defensively for a while. Try to catch Santa Anna when he's fighting Houston and provide reinforcements. Houston's leadership plus your manpower should do the trick until you can get your own leaders.
You will have to go into a massive economic deficit to win!
As soon as manpower points build up, build new infantry brigades. You will need reinforcements, and try not to lose any existing. You are starting out out-manned and out-generaled. Be patient. You will eventually gain the initiative and can fight Mexico to a white peace. I would recommend that starting out you accept and prepare for the next phase.
Your first research should be for Romanticism. You want Manifest Destiny early on.
For what it's worth.