Depends on the quality of the water jug. The Glass carboy from a supply store, is not porous, and great for primary and secondary fermentation. The PET or Better Bottle carboys are made from a thicker plastic for a water jug, and good for primary fermentation, debatable on secondary fermenation(won't get into that).
As far as the water jug, it may be too thin and porous. If I were you, take a stab at hard cider in that if you want to try it in that.
Are you asking about the flimsy plastic water jugs, or the thicker ones that look like carboys? If it's the thick ones that you turn upside down in water systems, then you probably could try it.