As you can see in the table, over the past four decades fewer and fewer GSS respondents of Mexican descent self-identify as white. In the 1970s, almost all Mex-Ams thought they were Caucasian. The drop could be due to fewer recent white Mexican immigrants and/or due to a reduced tendency to call oneself white.
This table shows that while the percent of blacks and "others" who are Hispanic is on the rise, the percent of whites who are Hispanic has stalled or is dropping.
Television programs and college ads in Mexico (see Steve Sailer's post) show that being white is popular there, but a recent study published in the American Sociological Review reported that as Hispanic immigrants spend more time in the U.S. and learn English, they are less and less likely to self-identify as white. The authors interpret this as immigrants encountering so much racism here, they begin to see themselves as Hispanic since the country won't let them be white. There could be some truth to the claim that America has a narrower definition of white than in Latin America, but I suspect that the finding also reflects that, while whiteness is popular in Latin American countries, being a person of color is popular here and carries with it financial benefits. (The study also shows that darker-skinned Hispanics earn less, and, of course, conclude that this proves racism, and, of course, fail to mention the possibility that skin color might be a rough indicator of genes that predict economic success).
I take the trend of turning away from whiteness as a sign that a majority of Hispanics are assimilating toward a victim class, rather than merging with the white majority. This squares with their consistent two-to-one voting for Democrats.