Atmospheric water generators (AWG) would be particularly helpful here. Rainwater harvesting and indoor farming would also be major contributors to the livelihood of your population.
You mentioned that your world is post-apocalyptic. So, are they the only people left (at least in the United States)? Is national trade available? If not, then your people should have a notable focus on canning and preservatives. Some foods will not be available year-round even after taking that into consideration. Somewhat secondary, you can factor this into the seasonal economy of your population.
Another strong consideration are GMOs. Plants can be modified to increase the amount/size of the fruit. They can also be modified to withstand the harsher climate of the desert. Your population can even create entirely new species of plants that never existed before. Animals can be modified to breed faster and have larger broods.
Ideally, for this community to be sustainable, they would have to be resourceful and have a fair knowledge of agriculture, engineering and science.
Additionally, here is a very short list of just a few plants and animals that have evolved to endure arid/semi-arid environments. I just wanted to give you some valid examples:
considering the fact that the world is post-apocalyptic, there is a decent chance that some animals not normally found in the Nevada desert might migrate there
Also, for more diversity, you might want to consider extending your population pass the Sierra Nevada and Cascade mountain ranges. One of the main reasons for any group to venture out and migrate is because of a lack of food. That's why there's very few large cities in deserts. Historically, people gravitate to areas that are abundant and rich in resources, which are usually areas that are close to the ocean. Is there a reason why they're stuck there?