Happened to me last year in ORD. I knew it was my fingerprints because there was some sort of error message on the screen but it flashed really quick and I couldn't really see what it was. I took the "X" receipt to the nearest CBP officer and he asked me if I knew why I got the "X" so apparently there is no code on the receipt to indicate the problem. Anyway he asked me a couple of questions about cash, food, etc. and then told me I could go. I received an email a few days later asking for feedback about my experience. I provided the feedback and this was part of the reply I received from the Program Manager:

"Thank you for taking the time to provide feedback on the Global Entry program. We apologize for the difficulties that you encountered while using the Global Entry kiosks to enter the United States on February 22, 2010. On this date the kiosk failed to grant you passage, because your fingerprints were not properly recognized; the images captured by the scanner on this date were of poor quality.
We endeavor to improve the quality of the program and are examining alternate means of verifying the identity of program members. In the interim, please ensure that your four fingers are properly placed on the fingerprint scanner when the images are captured. This will allow the scanner to obtain a more accurate image of your fingerprints. We are also making modifications to the system to allow for a second attempt at fingerprint capture, should the first attempt fail."

You may receive a similar email.