June 7 is now the official date for the firmware update, in Japan at least. That happens to coincide with Nintendo's E3 presentation, so we're now expecting that to be the worldwide release date, so Nintendo can make a dramatic reveal on stage. We're checking with Nintendo, in any case.
Update: The update will come to North America "the evening of June 6 Pacific time," according to Nintendo's website. Thanks to Donald for spotting that.