I checked out some info on Tanami Track, and it is indeed a little rough. Not much wiggle room if something goes wrong. I would figure with the heat of the place, you would need at least a gallon of drinking water a day. That said, it seems if you were able to press on decently each day, you might be able to plan to make it to a water source at least once a day, with the last stretch being the sketchiest..
I've been considering doing a Mojave and Death Valley tour, and have been researching ways to take more water, such as up to three 1.5 liter bottle cages (Blackburn Bomber, Topeak Modula XL) and an extra square gallon jug on the back rack. You would either have to get used to the extra weight/drink it quickly/or jettison gear or pack pretty light. My challenge won't be finding water so much as not having to find a source each day, allowing me to stay away from "civilization" longer.
I'd like to hear of someone being able to do this though, as it sounds like a challenge I'd be willing to try...