I spent a lot of time in the "country" when I lived in the Southwest. I wasn't what I call bird aware back then, but there are lot's of small birds around anywhere there is water in a for real desert. It is illegal to camp or stake out within 50 yards of a waterhole, although you can go to it for short periods. This is to protect the wildlife that desperately needs that water and won't come to it if people are around. In the mountains or near streams, where there are real trees, there is more water, and more birds. The place to look for them is in the trees, even small trees. And if you sit still for awhile, they will eventually come closer to check you out.
I worked in the oil field out of the 4 Corners area and have been to places most people will never see, or want to, although it's all accessible by any decent pickup or all wheel drive. There are dirt roads everywhere in the desert. Just get on one and follow it. Some of the most amazing back country can be found by following those roads and it's not in parks and it's open to all. If you are driving and get the chance, go up on one of those big plateau things. There's probably a road going up there and a couple of wellsites at the end of the road. There is also some of the most spectacular scenery you will ever see. I have seen water sitting in depressions of boulders on top of these things, and bees and birds using it regularly. And these little depressions with water are common. At 8 and 9 thousand foot elevations, it rains more than most people realize. But there is more small wild life than you might imagine if you just look for it. 
If you go to Google Maps and put in this link
, it should bring up a satellite map of an area that is very cool to visit. You can see all the little light colored squares on the map and all the little lines going to them, those are well sites and roads. If you zoom back out, you will see some of those mountain plateau things I was talking about. I was all over this area for years. If you ever have the chance, check it out, and keep your eyes open for cliff art, cause it's all over the area.
