Why would they even try that sort of migration? That is at least a thousand miles across some really harsh, as in jackrabbits need to carry food in a backpack to make it, terrain. Brutally, killing heat and dryness in the summer and frigid cold in the winters. Survival in the Sonora and Chihuahuan Deserts or even the slightly less foreboding Big Bend and White Sands deserts is almost entirely dependent on knowing where the water sources are, Those water sources tend to be defended by tribal bands at least as tough as the Nahuatl speaking population in Mesoamerica, and the locals would be fighting on their home ground. After summers that are beyond anything seen in Mesoamerica, any migration will now run head on into the High Plains in winter. It is entirely possible that no Aztec ever even saw snow, except on some far distant mountain. January in West Texas, or even in the White Sands Desert, will be completely outside their frame of reference. They will need to survive at least two, probably three full years of absolute hell before they manage to hit the Mississippi Valley. When the do, it won't be as the powerful Aztec state the Spanish found, the culture that dominated Southern Mexico for a couple centuries, it will be as a group of footsore stragglers that will find themselves facing well established Bands, maybe not at the peak of the Mississippian Culture, but still well established, quite aggressive and more than willing to do what it takes to defend what they have.
It is worth keeping in mind that it took American settlers and troops, using gunpowder weapons and artillery, with horses and wagons the better part of a century to handle the Tribal Bands of the Great Plains, and that was AFTER the Great post-Contact Pandemics gutted those Bands.
Seems like a long way to walk to encounter vastly worse conditions and potent adversaries than to settle in better terrain, in known climates a thousand miles closer to the starting point.
