I saw Michelle Obama had tweeted about this yesterday and meant to investigate. Not sure I can cope with the number of cheese-based puns in that blog post but I like the idea.
However, the proper Big Block of Cheese Day (by which I refer of course to the one in The West Wing, not the actual one in real life, which this event is modelled after) isn't just about the citizenry engaging with the White House but with small (professional) lobbyist groups who wouldn't ordinarily be able to get face-to-face access to senior White House staffers. Worthy causes, not lunatics on Twitter.
That said, I share the nostalgia, particularly for the second Big Block of Cheese Day when Margaret vehemently denies having carefully matched anyone up to their guests (still looking for a YouTube clip, from BBoCD1, where Toby correctly dubs this 'Throw open our office doors to people who want to discuss things we could care less about .. Day').