I wonder how Las Vegas would exist in a local resource system. Talk about a poorly placed city.
This is going to be off topic, but I can't resist.
In the years before 1920, artesian wells in the Las Vegas valley shot water over 6 feet in the air. Early settlers had no problems with growing enough food for themselves and their livestock. In the early years mining was an important industry (and actually still is active, although not as important as in years past), as well as services to travelers to southern California. (In a rational world, mining would be a more important industry than it currently is, since just to the south west of Las Vegas is the only source of rare earth elements in the U.S.; the mine was shut down in 2002, and since then all the rare earth elements have been imported from China).
In the 1930s the construction of Boulder Dam led to a big increase in population, but could have led to a great increase in the water supply, if not for the unfortunate (for Nevada) history of the negotiations for the water rights to the Colorado River.
In 1922 seven states met to negotiate the rights to distribution of the water of the Colorado, but the representatives from Nevada were all from the Reno area, leaving Las Vegas unrepresented. The story goes that the California representatives plied the Nevadans with whiskey until they were too drunk to participate, leaving Nevada with a pitiful share (4%) of the Colorado water.
The subsequent history of the growth of the gaming industry is perhaps better known. I do not dispute that it left Las Vegas overwhelming dependent on the entertainment and hotel industries, with the ups and (currently severe) downs experienced by all tourist destinations (Hawaii is currently experiencing a similar decline in visitors), but is that qualitatively different from other one industry towns like, for example, Detroit?
In fact, I would argue that with the absence of an income tax, and a state government far more business friendly than its neighbors, Las Vegas is far better positioned to recover than a city like Detroit.
Getting back to Frogboy's point, while I think I've established that Las Vegas could have been a successful, self-sustaining small city absent outside support, there's no doubt that the real world "global resource" system, where food and other goods can be imported, was the only reason the city was able to grow as large as it has.
Note: technically, Las Vegas is not actually all that big. The whole southern and southeastern part of the valley is the city of Henderson, where I live, and the "Strip" and a good part of the central and western part of the valley are in Clark County, but not in the city limits of Las Vegas. Again, the growth of the Strip and the relative decline of the downtown Fremont Street businesses has a lot to do with the lower taxes and looser regulatory regime of the county versus the city.