Interesting Question
I like this question. Very interesting.
With the overwhelming destruction wrought by the Civil War, I can't see a large-scale war breaking out with Mexico in the 1870s. And even if it did, the US could not hope to occupy and permanently subdue the Mexican, mestizo and native populations of northern Mexico. Won't happen people. It would be a temporary occupation, at best.
If you read your history of the Apache Wars, the Mexican Army (like ours) used native americans as scouts and soldiers. In this case, the Mexican Army used the Tarahumara, much like the U.S. Army used the Navajo and Apaches. Sending a conventional army into the northern Mexico Sierra Madre mountains (either range) would have been akin to suicide. Sending the US Calvary with Navajo/Apache scouts would a wiser choicer but it would still be a very bitter fight, in my opinion. The US Army could take the major cities and flat lands with no problem. But fighting and rooting out the Mexican army (in their own back yard), along with the Chiricahua Apache, Yaqui, Tarahumara, would take years to complete. They'd blend into the mountain terrain (which is rough as hell by the way) and employ hit and run tactics (does Pancho Villa or Geronimo ring a bell?).
However, I don't know the US had towards attitudes towards Mexico during the 1870s.