> And what happens if a thousand people show up and there is not enough of that limited resource in the desert for all of them?
By the time water and bread are this rare you have long stopped thinking in economic terms, armed yourself and probably got killed. If it is a temporary outage, you can count on people to help each other.
> Without controlling the number of people drawing from said resources you will over load the system
From an economic point of view we don't have to worry about food and water, just about its distribution.
Realizing that I'm going halfway Godwin on you here: "Controlling the number of people drawing from said resources" is a very.. weird thing to say when the resources in question are water and bread.
You are over-generalizing the "basic necessities/basic income" to "resources". People who only have their "basic income" won't be able to purchase rare resources, they just won't have to worry about a roof over their head, water and bread. Why does everyone assume that people don't want more? You want to go on a holiday? You work. You want that bigger TV, a car or just a new game? You work.