It's one of the few ground covers that will thrive in the Sonoran low desert. The more you water it, the better it looks, but it will hang in there during your New Mexico drought if you are not watering it. When it gets drought stressed, it tends to leave lots of bare spots, but since the stolons are so deep, it can regenerate once it gets frequent rains or waterings.
Other possible ground covers are
Abronia villosa, the Desert Verbena, which is not considered native to New Mexico, but which does well in the Sonoran desert. The reason I keep mentioning the Sonoran low desert is that with the anticipated changes in the climate, the high plains of eastern New Mexico may begin to look more and more like the desert between Phoenix and Palm Springs. If you select species from that area to plant, they will be used to 4"-8" of rainfall and will tolerate the drought you are going through.
Another possible planting is
Curcurbita palmata, the Coyote Melon. Like other squashes, it covers the ground with big leaves and keeps the wind from blowing it away. It needs more water than the verbena, but where the water tends to puddle up after a summer thunderstorm, it can go off to the races. Although the flesh is too bitter to eat, you could try feeding it to chickens, they will go for the seeds and might even like the flesh.
These two aren't exactly garden center type items, but if you look online, you can find the seeds from places specializing in native desert plants.