I know a small percentage of Mexicans are actually descended from The Mexica themselves. Through the colonization of new Spain indigenous practices that were foreign to other indigenous people have now become traditional. What aspects of your everyday Mexican can be attributed to the Mexica?
The vast majority of those who live in modern Mexico are the direct descendants of those who lived in the area prior to European discovery (not just Aztecs, but other ethnic groups as well):
http://www.ucsf.edu/news/2014/06/115251/mexican-genetics-study-reveals-huge-variation-ancestry
The language spoken by the Aztecs, Nahuatl, is still spoken in Mexico today, with over a million or more speakers:
http://www.houstonculture.org/mexico/nahuatl.html
So there are plenty of people with direct genetic and linguistic ancestry.
Isn't Aztec a political designation rather than an ethnic one?