Clearly, to adhere to our style rules, F.D.R. should have said “that.” This is a restrictive clause defining the “date” we’re talking about. (In fact, the Columbia World of Quotations, among other sources, renders the quote incorrectly online, substituting “that.”)
Perhaps Roosevelt thought, as many writers and speakers seem to do, that “which” sounded more elevated or powerful. Or perhaps he was influenced by British usage, which often employs “which” in restrictive clauses. In any case, we’re prepared to allow an exception here.
