You would have to be hauling arse to cross in 2 days... take your time mate, enjoy the desert. I also agree that there is no way I would do it alone with 1 car.
We did it a few years ago, but East to West (the harder direction), and the desert had just re-opened after all the rain (we were the first group to cross), so it was pretty hard going. Took us 4 days Birdsville to Mt Dare.
And hows this - I did it in a rental car! A Britz 4wd with roof top tent... had to repair 1 tyre, and we had to tackle 1 long deep water crossing. There were also some detours due to the rain damage and swollen creeks - we had a mud map from the ranger at Birdsville.
So - as already mentioned, a tyre repair kit including plugs and patches. Tyre levers, a solid ratchet strap to help re-seat tyre beads, and of course a compressor. Long handled shovel - absolute must have. Its sand, so with some patience and labour you can dig yourself out of almost any stuck.
Carrying ULP inside tha cab is a no-no... on the roof is better, but still not ideal (diesel is OK, but ULP up top is not recommended). Get it into your tank asap as soon as it will fit.
Always pretty good info on these types of trips on ExplorOz, including fuel usage for different engine types and sizes etc:
http://www.exploroz.com/TrekNotes/De...on_Desert.aspx
LOTS of info on fuel usage here:
http://www.exploroz.com/TrekNotes/TrekFuel.asp?TrekID=2
S.
ps. don't forget to get your permits etc!