If you are heading down to El Paso for a "look" I would route from Amarillo to Roswell, NM. You gotta check out the home UFO's and Aliens!
Unfortunately you can't cruise down to Carlsbad to visit the Caverns due to the government shutdown.
From Roswell you can go through Ruidoso, NM, very cool mountain town (Inn of the Mountain Gods) and its a nice drive from there on into El Paso.
Have fun guys!