I'm not positive on that one. I know there are some, but they can be few and far between. I think it really all depends where you are at, food, water, etc. Water is the main point. It is really dry around there, so I would focus on finding some water. How far away from Clovis are you looking to hunt? If it were me, I would be looking out towards Tucomcari (N and W of there as well) and Ruidoso. My uncle has shot some really nice bucks around Carlsbad, but they are hard to find as well. I would say your best bet is rifle hunting around Clovis. It is pretty open and fairly flat around that area if I remember right, but it has been several years since I have been through there.
I went to college at Hobbs, NM and we hunted dove and quail like it was going out of style. Never saw any antelope and saw some decent deer, but they were scarce... of course we weren't really looking for them either so maybe it wasn't that bad.