How anonymous is anonymous?

When a journalist attributes a quote to "anonymous," how much information can be revealed? This NYT Magazine piece on Senator Rick Santorum has a quote from "a Democratic senator who would talk only on the condition his name not be used." Did this anonymous source say, "Don't name me, but it's OK to reveal my job and my gender"? What if it were an anoynymous source from a smaller workplace, where simply knowing the workplace and the gender ("he said," or "she said") would make it easy to track the source down?