I'd have to say the sun gets really hot so I doubt it is overwatering. Try an experiment. In the same location plant three plants in two different spots, water one trio once a day and water the other every other day, put a stick in the ground and label 1 and 2 and see for yourself which survives and if they both do then water every other day under the same conditions but if they are out in the open then water once a day in the evening. Just buy a 1/2 a dozen first. Make certain the soil is amended thoroughly.

Here is a link that might be useful: Propagating Perennials

In NM, I imagine the summers get pretty hot, even at higher elevations. During the first year, even the most drought tolerant plants need water to get established. I agree with the compost. I mix leaf compost in with my thyme. We had severe droughts for the past two years, which were just broken by some heavy spring rains. Our creeping thyme was looking a little dry and spindly last summer, but this spring, it bounced back to life. Be patient and water for the first year or two.

I have a succulent 'lawn' that is absolutely fine under heavy clay and abusive situations. Perhaps you should mix the two.

Suzq, could you tell me what type of succulent lawn plants you have? I have heavy clay, hot dry summers, but am zn5 and would love to try it!
Thanks~Vic