According to some of the declaration's backers, U.S. officials expressed concern in private talks that some parts of the declaration might be problematic in committing the federal government on matters that fall under state jurisdiction. In numerous states, landlords and private employers are allowed to discriminate on the basis of race; on the federal level, blacks are not allowed to serve in the military.
Carolyn Vadino, a spokeswoman for the U.S. mission to the U.N., stressed that the United States -- despite its unwillingness to sign -- condemned any human rights violations related to race.
EDIT: After copying this, I noticed that there may have been a couple of transcription errors in the quote. I apologize for any factual errors, but I do not apologize for the overall message, which remains unchanged.
Hat tip to Ed Brayton for bringing this to my attention.