There's overdosing (to the point where you risk it being lethal) and then there's general ill effects. Even as someone very light (OD dosage is based on your weight, unsurprisingly[1]), it would require me to take multiple caffeine pills before I'd have to potentially go to the hospital: I simply couldn't do it through coffee alone - it's just too much liquid to consume in too short a time. Even with crazy-strong coffee (250+mg/cup) I'd need to drink 30+ [2] cups.
But you can bet your bottom dollar that drinking a dozen cups of coffee by lunchtime will have some pretty interesting results. You'll feel your heart racing and probably experience something like extreme ADD. Probably headaches, nausea, crazy jitters. The severity depends on your tolerance to caffeine, of course. I get nasty headaches 6-8 hours after waking if I don't get my morning coffee, so it takes me quite a lot to get into overdose land.
[1] https://en.wikipedia.org/wiki/Caffeine#Caffeine_intoxication [2] ~150mg/kg for LD50; I weigh about 50kg