America Buys The West From Mexico

  If its the same territory in extent and Mexico can be persuaded to sell then those who died in the conflict and their TTL descendants live and hence probably a fair number more people alive by now.  Selling such a huge amount of national territory would be a huge issue for Mexico however so I'm not certain it would be a practical idea.

  If it did go ahead you probably have somewhat better relations between the two countries and less resentment at the OTL US invasion of Mexico and annexation.  How many butterflies this has I don't know.

  One possible significant factor.  Without a war over the SW and with expansionist encouraged by Mexico being willing to sell such lands do they demand all the Oregon region say, which is likely to mean war with the UK.  Which is going to be costly for both sides but potentially very bad for the US.  Britain hasn't had the experience of the Crimean war to clear out some of the dead wood in the military but still has a markedly larger starting army, let alone navy and greater industrial and fiscal base. 

  Also with Britain having ended slavery in 1833 - assuming we're talking of a clash in the late 40's - could that become an issue if British forces start landing in areas in the south.  That might moblise the south which otherwise is likely to be opposed to such a war but could make things a lot more bitter, especially if ending slavery in the US is sold as a moral crusade in the UK.

  If we avoid such a conflict and assume something like an OTL partition of the territory it could well be that the US still ends up buying Alaska so probably not great butterflies from OTL other than from those extra people being alive and what they might throw up.

  Almost certainly in both cases.