Lisa...

It could be the caffeine, but it could also be the stimulation from the hot beverage itself. Many older ladies when I was growing up, my grandmother included, swore by a cup of hot water first thing in the morning to produce their daily "physic" as they referred to it.
If you do find yourself constipated and extra water and fiber don't do the trick, be very cautious with using laxatives. Only use them when absolutely necessary and nothing else has worked. If used too often, your body can become dependent on them and you will find yourself needing them more and more frequently. I've seen many patients in nursing homes completely dependent on laxatives to produce a bowel movement after years of abusing them; they simply couldn't go without them.
Sometimes just adding more fat to your diet will help things start moving along more smoothly (pun intended).