Mexico would likely become yet another country under occupation until a government that the US sees as acceptable is set up, similar to Japan after WW2. I can't see them being annexed, most of the American public would be vocal with their disapproval of annexing a country we were at war with.
Border security would probably become even more extreme, as we don't want a) their refugees, or b) anti-American extremists jumping over. In the distant future, it may lessen as tensions disappear because the government put in place was put in place by the US.
The American economy would likely improve a little as we would be fighting a homeland war, and jobs will be created to fuel the war effort and reconstruction.
The long term effects could be similar to what happened with Japan: an old enemy has their society destroyed and rebuilt into a powerful ally, which becomes beneficial for both countries.
All said and done, an all-out 2nd Mexican-American War could be a good thing in the long run, assuming things go well.
This is just a theory though. It's possible that the US might simply abandon Mexico after a war, however trends starting with WW2 and running through the Cold War into the 21st century show that this would be extremely unlikely.
there needs to be context though. a war for what? land? drugs?
does war even need a reason anymore?
