As long as the barrels are "food safe", clean, and nothing gets in (dust, dirt, etc), the water can easily be stored for a week or two, most likely longer. I make my water on Sundays for use the following Saturday. I've let it go longer during vacations with no ill effects.
I would keep it out of direct sunlight/heat sources, etc, to prevent any micro-nasties that were in the container from blooming.