This report from the Pew Research Center discusses the growth in the Mexican-American population in the U.S. Immigration is no longer the major factor; the birthrate is.
The study notes:
The pattern from 2000-2010 was a change from the previous two decades, when births to Mexican-American mothers in the U.S. were matched or surpassed by the number of new immigrant arrivals.
The birth trend is largely attributable to the surge of immigration from Mexico in recent decades. The report uses data from the Current Population Survey taken by the Census Bureau, as well as Mexican government data on migration of Mexicans in and out of that country. Immigration to the U.S. from Mexico ebbed in the 2000s compared with the 1990s.