A lot of the Mexico campaign as written suffers from "the map is not the territory" problem. The narrative of the campaign relies on looking at flat maps with highways and state borders and assuming the land is just as flat and featureless. The land of the Southwest is rarely flat and featureless. In fact the settlement patterns and placement of cities in the Southwest was basically determined by low altitude passes through mountain ranges and access to water.
Mexico invading southern Texas? Yeah there's not a lot of movement-stopping geography. The Sonora Desert portion of Arizona and California? Also makes sense. Invading up to Bakersfield? Not a chance. A Boy Scout troop could secure the Techapi and Tejon passes into the Central Valley. The Mojave desert is a barely habitable moonscape, no stretched thin army is going to be holding it. Northern Arizona is likewise not a place an army with long supply lines in a resource-scarce setting could manage to hold. New Mexico has a couple valleys stretching north-south and holding those would be difficult as well.
A nuclear beleaguered US would have a hard time securing its southern border. So an invasion by Mexico could gain ground for sure. It's just not a friendly region without pumped in electricity, power, and food. A small invasion force would be hard pressed to maintain LOCs and make forward movement.
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