Swamp Cooler A/C
Yes, there must be water available to the unit in order to cool. 'Swamp' coolers work on the principal of evaporation. That is, air is drawn through or pushed through a wet media, and the process of evaporation absorbs heat, resulting in a small drop in the temperature and increase in humidity of the air so processed. Best case amount of cooling would probably be 20 degrees or so, depending on the humidity of the air coming in. The higher this humidity, the less evaporation occurs and thus less cooling. Holes in or around the media also reduce the effectiveness, as any air which is not exposed to evaporation, is not cooled. Finally, the media usually needs frequent replacement or cleaning, as any crap in the water is left on the media after evaporation, which can clog it up so water and/or air can't get through.
Also, swamp coolers never recirculate air, so you must have a way for the air to exhaust to the outside rather than back to the cooler. If not, the air will just get higher and higher in humidity until no more cooling can take place. The opposite of AC, the more windows you have open, the better a swamp cooler works
Portable swamp coolers either get their water from a built in tank, or from the RV water system. Check yours to see whether there is a filler opening, or tubing coming in. Some use capillary action or gravity to wet the media and others use a pump or the pressure of the water supply. Like the media, this system can get clogged by stuff in the water. Verify that the media is being thouroughly wetted.