The demo of Mortal Kombat: Shaolin Monks has actually in stores for quite a while - August 9, officially. Unofficially, some lucky people got it earlier, and some later. By this time, everyone in the U.S. should have fairly easy access to the demo at stores near them. Check out the pics below in case you need help in finding which issues of OPM or OXM to look for:

Unfortunately, the demo discs are not identical. The PS2 version is very rich in special features, including a short image trailer which shows off some of the cool artwork from the game, and a really nice "Behind the Scenes" video which will probably be included in the final game. Presumably, the extra features are included in the PS2 version to make up for the someone toned down violence in that version of the demo. While X-Box users get to enjoy all the blood and gore of the final version, PS2 users will see black blood instead of the normal red. In addition, Fatalities and some of the more graphic cut-scenes are censored out as well, as can be seen in one of the pics below.
Overall, this game is very enjoyable no matter what system you're playing the demo on. Check it out in stores everywhere, and good luck finding all of the hidden secrets!