Some madman started a 7 player game at thirty minutes to midnight at GenCon. As I understand from my friend who played in it, it started to slow down at 3am or so, but more from the hour than the number of players.
I've run a very successful 6 player game and the only issue I found was screen time. So keep the action moving (as JBMannon noted) and be aware of switching your attention among all the players.
At this size, I'd consider using some sort of card system to keep track of who's been in the spotlight. I've seen the <i>Marvel</i> system applied to DW in this way: everyone has a card face-up in front of them, when they get a "turn" (which may be multiple moves) in the spotlight, they turn their card face-down. When all the cards are face-down, flip them all.
I essentially do something like this in my usual 4 player games, but I keep track of it all in my head. At 7 players that gets trickier.