Around AD 1300-1400, various Uto-Aztecan-speaking groups ("chichimecas") migrated south from what's now the western United States. Some of these groups travelled as far south as the Valley of Mexico, where they assimilated into the local culture and eventually rose to dominate the region via the Aztec Empire. Around the same time, but a bit to the east, the Mississippian cultures experienced some sort of partial collapse, as evidenced by the abandonment of their metropolis, Cahokia. I would be curious to know if that there is any evidence that these events were related.
For instance, could the collapse of the society centered around Cahokia have caused political chaos that the proto-Nahua fled from? Or could the proto-Nahua have occupied some sort of economic position in Missippian society which they lost in its collapse, sending them south towards greener pastures?
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The Mexica were merely the last in a long line of chichimec groups that migrated (Smith 1984). These groups began migrating in the late 600s/early 700s and may have had an impact on Teotihuacan and its abandonment. These groups were also responsible for integrating with local Otomi people to create the Toltec city-state as well as helping to form many of the numerous city-states found in the Basin of Mexico before the arrival of the Mexica.
That being said, if Beekman and Christensen (2003, 2011) and Beekman (2012) are right in their hypothesis that these groups are migrating out of the Bajio region of Mexico than the impact of Cahokia's abandonment on these groups in the Postclassic would be negligible.
How Cahokia may have impacted the US southwest is something I am not certain about and I have not yet had the time to dive in and research this other user's question.
If you are interested, I went into more detail about the location of Aztlan not too long ago.