I experienced the same thing last night. Searching around, it seems it's happening to lots of people. It affects the volume down button at the same time. A reboot fixed me as well. Holding down the volume down button and power button for more than 7 seconds (ironically the two buttons that aren't working) will cause an immediate reboot. Then choose the normal boot option. That's the only real issue I've seen. This was after the recent SW update from Verizon for the phone (released a couple days ago).
Af6nm, we are glad to hear that you were able to get that button to respond again. We all want you to be able to power on and off your phone as needed. This matter has indeed been sent up to Samsung and they are planning to release a fix with the very next software release.