With current plans underway the water supply has been estimated for at least 50 years of sustainability and that was assuming projected growth. Of course that doesn't include any future technology and conservation efforts, or if the building stops now. I really don't imagine growth being stopped until the limited land runs out here, and besides, it would only be shifting the problem elsewhere.
While the drought has eased for the moment in the southeast where you're from, it was a wake up call for better management of water resources there as well. It looks like it's also being called water wars there.
Vegas isn't alone on this end of the country, water shortages are facing all of the western states...
The shortages even occur in the northeast, and this one example from a few years ago.
Fortunately Las Vegas was studying water supply long before the drought and climate change that is effecting so many areas today, even in much wetter regions. Las Vegas technically ran out of water back in the 90's, but has managed to more than double in population and expanded quite a bit commercially since then. I did a blog on Las Vegas water 'running out' and some of the myths and misconceptions.
For the good news this year, the April - July Colorado river flow forecast is projecting 9.7 million acre-feet, or 122 % of average. Lake Powell is expected to raise by 50' and the added available release of 15% should add 6' or more to Lake Mead level forecasts. It's not a sure sign that the drought is over, but a definite improvement over recent years.
One other water issue that is currently being addressed, Tamarisk or 'salt cedar', is an invasive tree along the Colorado River that is siphoning off more water than Las Vegas' tiny water allocation.
Under a new agreement, Las Vegas would be the first to gain additional water from any additional resources developed such as from the Tamarisk eradication project.
Water supply is something that needs to be taken seriously, not only in Las Vegas, but across the country. Many areas are having their supplies dwindling due to aging infrastructure and lack of storage capacity to simply the US population growth, and investment was overdue. The fact that Las Vegas has had to look at it's supplies long before it was recognized as a problem elsewhere, has caused it to be much more proactive and allowed for it's growth.
I can't give you an answer if the water was shut off to Lake Mead on how long it would last. Our water is very dependent on the amount of snow received in Utah and Colorado. Instead of a long explanation, here is an article full of references and charts to show the relationships of water levels at Lake Mead and the annual snow reports in Colorado --