Technically, they’re called the “Caroline Islands,” NOT the Carolinas, which may have been the point of the previous poster. http://en.wikipedia.org/wiki/Caroline_Islands
Though to contribute to this discussion… the ease of defending the Carolines rests, I think, on how much damage Japan deals to the US fleet once they open up hostilities. In one game I played, Japan barely touched the USN when they attacked on the third turn, so I (as the US) invaded the Carolines with 2 infantry, 1 artillery, 1 tank, and support shots from my cruiser and battleship. Japan had 1 infantry and 2 fighters on the Carolines (the recommended defense force BasileII mentioned). Japan opted not to scramble the fighters, and the US took the Carolines, only taking a single infantry as a casualty. Granted, this might have been more due to luck than to any strategic considerations, but to my mind, it calls into question how effectively that small force could hold on to those islands, particularly in the face of a dedicated US push (and a mostly-intact USN stationed at Hawaii).
My assessment may change, however, once I’ve gotten some more play experience with the game. I will readily admit it may be too early for me to judge (the aforementioned game was only my fourth, and the Japan player was playing Japan for the first time, as well as pushing heavily to Alaska and Australia, leaving the central Pacific more or less open).