Leaving a damp towel for a week increases the risk of bacteria building up which may cause a respitary problems to your cham. Change at least every couple of days. It's really easy doing a drainage system > just suspend your cage about 5 - 6 inches off the surface where it's standing, poke a few holes in the bottom of the cage, and place a tray/container beneath so that the water drips into it..all you will need to do is empty the tray/container when it's full.
You would need to replace a towel daily. I would recommend putting a couple small holes in the bottom of your cage with a drip pan under it to catch the water. If there's still some water standing you will need to wipe it out with paper towels as mentioned above.