Shouldn't do this to create any more competition... but "like" NEXT on facebook- they release several (5 or so) same day tables pretty much every morning with an email contact option- no going through the site. They are usually tables at 5 and 6 oclock but sometimes later ones.
Update: Just checked and this is what was posted 45 minutes ago:
Same Night Tables available for tonight, Sunday, May 22 -
5:30pm - 2ppl
5:30pm - 4ppl
5:30pm - 4ppl
9:00pm - 4ppl
9:15pm - 2ppl
10:00pm - 4ppl

$100 per person plus pairings - email samenight@nextrestaurant with phone number, pairings option and which time you are interested in.
Cheers!