Debate about the actual human carrying capacity of Earth dates back hundreds of years. The range of estimates is enormous, fluctuating from 500 million people to more than one trillion. Scientists disagree not only on the final number, but more importantly about the best and most accurate way of determining that number—hence the huge variability.
Every time we've run into issues, we've innovated our way out of it. We build dams, improve irrigation, seed clouds, desalinate water, etc. I see no reason for this to stop.
There's probably a theoretical limit, but population growth is slowing, so I doubt we'll actually hit it. Likewise, space tech is improving, so we'll probably expand outside the planet as well, which will also result in more innovation for supporting populations on limited resources.
For Vegas, the main concern is water. Energy is cheap and can be much cheaper, so air conditioning shouldn't be a major concern. In fact, it's probably better for people to live in deserts because that's (likely) less of a strain on wildlife vs living in forests or swamps.