I hiked the HST in Sept, 2012, another dry year, and there was no trouble with water. Looking at the map, I would carry no more than a liter for most sections, making sure to drink as much as possible before leaving any water stop.
If you spend the night on Whitney, you should take at least 3 liters up. What worked for me was to carry empty quart freezer zip-lock bags, only using them for the Mt Whitney overnight. I filled them, put them inside a gallon zip lock, and placed them gently in the top of my pack.
