People can survive for about 3-5 days without water. If they weren't travelling with water they are probably close to the upper bound of this. Its entirely credible.
One possible scenario is that they suffered a mechanical breakdown in a remote road or wash, similar to the Death Valley Germans. If they had, say, a 5 gal jug of water in their car (as one should, if headed into the desert), they could survive much longer if they remained with the car, did not eat, and did not exert themselves.
Priority obviously needs to be locating the car, which aerial searches are pretty good for.