There are to many Mexicans, if you're referring to illegals of Mexican citizenship. I'm an American who is Hispanic, and I prefer to be called an American who is Hispanic. And, I prefer to be hired because I'm the best paint mixer Home Depot can find (which, if you've ever bought paint at HD, they've never been successful in finding, BTW) and not because I'm an American who is Hispanic. But, if you see me mixing paint at Home Depot, I guess you'll never know now that the La Raza crowd has pulled this .
There are a lot of American hispanics in my area of Michigan. Most are second and third generation Americans whos parents came to work in the Willow run bomber plant during WWII.
Some of the names are no longer hispanic due to changing it to become more American. My great grandfather changed our family name to make it appear more American in the same way.
If they were American Mexicans, they'd just be just plain Americans.