I have hunted Texas before and they have mostly whitetail, there are some mule deer along the New Mexico border. If you want over the counter tags look at Colorado.
Ace
Depending on where and how much? You could check out the NRA Whittington center in Raton New Mexico, I have hunted there for Elk, and saw some nice Mule Deer. I have not hunted Jirralla Reservation before, but they have nice photos of Big Mule Deer.
Ace
Give Festus Farrington a call 575-517-0691. He had offered me some elk tags last year the week before I was leaving for Colorado to hunt Muleys and I could not make the hunt in New Mexico.
Ace
Give New Mexico a call several of the Reservations offer hunts for groups or singles. Try Acoma, Zuni, Jicarilla or Mescalero they may have what you're looking for.
Ace