Northern Arizona has a sizable Mormon population, which tends to vote Republican.
Southern NM, particularly SW NM is sometimes called Little Texas.
That's East New Mexico - far northeast as well as southeast. Basically what shows the largest swing here:
(2000 presidential and 2002 gubernatorial. Harry Teague's 2008 House win also depended on Little Texans' penchant to occasionally desert the GOP en masse. Though obviously not, not in a long time, in presidential elections.)
Meant to say SE and typed SW for some reason. I stand corrected.