Whether or not large populations powered by the Three Sisters can exist is fairly well settled by all the pre-contact cities and large towns in North America which did exactly that. But could this work where Las Vegas is now?
Las Vegas was not always a concrete jungle in the middle of a desert. Human activity desertified the region. If your apocalyptic scenario reverses that (blow up some dams, screw with the weather, whatever), you should be good.
You also mention livestock, which pre-contact cities lacked. Add early 19th or 18th century technology, and you're pretty secure in terms of food supply. The question you'll eventually get to is agricultural innovations, such as certain fertilizers and pest control. For instance, is the corn you're using a variety with genetic modifications for pest resistance or high efficiency yields? Even if the tech to produce GMO crops is lost, the crops themselves might still exist, and without the likes of Monsanto cracking down on their natural spread, their natural advantages will probably let them spread very quickly until they hit geographic barriers.
The real question is just how large a population you can sustain, and that depends on loads of other factors. But Cahokia and Tenochtitlan had populations in the thousands, and the same three crops were the staples then and there. Seeing as you're suggesting better tech is available than what the Mississippian and Mesoamerican civilizations had, those should be considered a lower bounds on what's possible for your larger cities. It is, however, relevant that Cahokia is close to the Mississippi River, and Tenochtitlan was on a lake. You might have to blow up the Hoover Dam for the Las Vegas area.