New Mexico was majority Hispanic from statehood until the late 1940s, when Los Alamos brought in the scientists and cheap land brought in the Texans. Has only been majority non-Hispanic since that time, and Hispanics have had a plurality since the late 80s/early 90s.
According to the 2000 Census, 44.7% of New Mexico's population was composed of white Anglos, while 42.1% was Hispanic. It's possible that the 2010 Census will show a Hispanic plurality, but it's not there yet. BTW, only 5.4% of New Mexicans in 2000 were non-citizens, which is far lower than fellow border states California (15.9%), Arizona (9.0%) or Texas (9.5%).