I have the same problem, not from lack of coffee (which I drink a half-pot of every morning, and have since I was 14), but from lack of soda. I've tried to ween myself off of goddamned Diet Coke many times over the last couple years and I just can't, because by day three I always have a pounding headache. As someone that quit smoking cold turkey, after smoking a pack a day (Newport, no less, no piddly shit Marlboro Lights) the fact that I can't break myself of my Diet Coke habit drives me mad.
One would think I would be getting my caffeine fix from the java, but I'm definitely having withdrawal symptoms from something in the soda that is not present in the coffee. If not caffeine, what else can it be? The cola itself? Perhaps. All I know is within a couple days without my head feels like it's in a vice. I've gone similar amounts of time without coffee and suffered no ill effects, outside of being a fucking zombie for half the morning, of course. That's the other weird thing I've noticed: the caffeine in soda doesn't seem to have the kick for waking me up like coffee does. I lived down in Georgia for a time and the people down there drink Coke with their breakfast, but that was never sufficient for me to jump start my day for whatever reason.
It probably is all psychosomatic (well, not the headaches from the caffeine withdrawal, but the need for it to function like a normal human being before 10 AM) but regardless, the headaches are miserable so I'm stuck on the Diet Coke until I find a more healthy substitute.