An emailer brought to my attention that Greg Ransom apparently did a google book search on Keynes's "if the facts change I change my mind, what do you do sir?" quote, and sorted on date. He dates the printing of the uncited quote to 1940, which is earlier than I've ever heard it (I always heard it was first printed in the Harrod biography).
For some reason people get really worked up about the uncited nature of this quote (even Brad DeLong at one point, if I remember). Others take it to be a sign of "fickleness" or unsteadiness on Keynes's part. I find that view especially bizarre because the whole point of the quote is to say that what appears fickle to a critic isn't fickle at all if you realize that the ground has moved beneath you!
Anyway - I've always liked it, and see no reason to doubt it. It certainly sounds like something Keynes would say. We know he allegedly said it when discussing the import tariff at the Treasury in the early 1930s. Clarke calls it a "Cambridge oral tradition", which is probably where Harrod picked it up - he had been at Cambridge briefly, certainly was in contact with the department, and certainly talked with all sorts of people for the book. Since Harrod is dead, Robinson is dead, Pigou is dead, and everyone in the room at the Treasury that day is dead, I'm not sure what the point of fussing over it more than that is. Note that it's attributed (citing Harrod or whoever you want), and keep your eyes peeled if you're going through papers and correspondences at the time to see if anyone mentions it. Even then it will still be attributed.
Perhaps I would make an atrocious historian but I personally don't see much more to it than that.