If you've had period pain, you've probably tried NSAIDs — they include aspirin, naproxen, ibuprofen, and mefenamic acid — as the most common treatment for period pain, they're somewhere between 45% and 53% effective. However, a recent review of NSAID use for dysmenorrhea (painful periods) concluded that "women using them need to be aware of the substantial risk of adverse effects." Common adverse effects of NSAIDs include: stomach problems (bleeding, ulcer, upset stomach), high blood pressure, fluid retention and swelling, kidney problems, heart problems, and rashes.
For most women, if you have significant menstrual pain, it's lasting more than one day. There's a black box warning on the box of Tylenol that says do not exceed such and such a dose or you'll have put yourself in danger of significant liver damage.
So If you have round-the-clock cramps, once you get to 24 hours, you're probably pretty close to hitting the max for the black box warning, so you have to be really careful about that. When it comes down to it, you just can't take enough Tylenol to manage menstrual cramps that are going on for more than just a couple of hours.