The rush tickets go on sale when the box office opens (10am. 12noon on Sundays). Once they're out, they're out (though they may do Standing Room Only after). Sometimes you might be able to get rush tickets if it doesn't sell out in the morning but it's not as likely, especially during Daniel Radcliffe's final month in the show.
I just rushed it and thought the lines wouldn't start as early now that it got colder but I was wrong. I'd say 9am is safe, but to be really safe, 8-8:30. I got there at 8:15 and was already at the stage door. (It was a Sat with 2 shows available for sale though).
They do however seem to have a lot of rush tickets. And in the summer, I know people who lined up past the Japanese Restaurant still managed to get tickets (on a 2 show day again).
http://tapeworthy.blogspot.com