There is no 34 mile stretch without water on the entire CT.
From Baldy Lake to the first decent water on Lujan Creek is 12.6 miles. From where you leave Lujan Creek a little further down it is 19.1 miles to Cochetopa Creek. Los Creek is 9 miles from Lujan Creek and breaks that in half. Although it may not be much of a flow, I have always found water there. Where the trail does a hard left at mile 9.0 continue straight ahead on the closed road and follow the creek. The water gets better a few hundred feet up. If you keep going straight you will hit the trail again in 1/2 mile. That used to be the CT but it was rerouted because jeeps were getting stuck in the mud. There are some ok campsites in there.
I have done the trail multiple times and carry two one liter bottles plus a filter. I camel up - when I stop to filter water I try to drink a full liter before moving on. That gives you 5-6 miles before you have to start drinking what you are carrying.
The one place I would recommend having 3 liters is in segment 27 where you will probably have to dry camp near Orphan Butte in order to get over Indian Trail Ridge early before the afternoon storms.
bearcreek