Mexican culture is a fabulous thing. Sadly, a country that kills its own people isn't a fabulous thing. The USA has the strongest military in the world, all you would need to do is go and defeat he military and put the drug dudes in prison and -poof- yours for the Taking! The place is so tatally beautiful, with fascinating desert in the north and rainforest in the south. Who doesnt want a tropical place to hang?
Look Mexico is a corrupt nation that is falling apart. Plus, up here in America we have a serious illegal immigration problem. Why take the time to push them back into their own country, when we could just defeat their corrupt government, annex Mexico, make it part of America, and help the citizens. We'll have extra resources and more land, and all the citizens can become Americans.
They are going to jump either way so we might as well let them it is it will also solve drug problems we can search them too so it will be even then we wont have the problems that knocks out two birds with one stone. So that's is why
People who like to play conquistador forget one important detail: More territory means you need more personnel to guard your expanded grounds and more equipment. You are spreading yourself and your resources mighty thin. And do not forget, the people you subjugated are not going to forget what you did, so you will be constantly weakened by guerilla warfare. And other subversive activities.
Annexing Mexico will not solve the immigrant problem. It will mean that they are legal, but you'll have illegal immigrants from countries bordering Mexico anyway. On top of that, Mexico would still be for a time less developed and not up to scratch with regards to the rest of the USA, so people would internally relocate to the rest of the States. So in fact it would make the problem greater as not only are the immigrants still taking jobs, but they also are legalised. Plus you would need to accommodate 120 million extra people, so that would add an extra 1/3 roughly to the US population. And the majority of them are Hispanic/Latino, so the Republicans would have a jolly good time attempting to sway them over. Speaking of politics, imagine the Midwest states' uproar over their power being diminished? Or how the electoral college would look?
We annexed what is now Texas from Mexico in the mid 1800's. Though our US history books paint the Mexican American war in a different light, it was for the most part a war based on fabrication and a policy of Eminent domain to further US interest. The US offered to buy the territory from Mexico but, they decline; we just took it.