I have no personal experience to help you out, but a suggestion which might be worth looking at would be groopii, which is a hostel booking site specifically aiming at large groups, created by the same people who're running this site. I have absolutely no idea how swift groopii is with responding to requests (their tagline says "fast", but I have no idea how successful the site is, and thus no idea of how many people are working on answering requests), so I would continue looking yourself as well - but at least worth a shot to send off a request to them.
The other suggestion I have is to somehow find out what the largest hostels in Paris are (maybe you can get your hands on a lonely planet for france/paris?) - it's high season, so I'm expecting only the very largest hostels to be able to accommodate an extra 14 people on very short notice - and just call them (good thing with large hostels is that they should also have 24 hour reception).
St. Christopher's Paris comes out as the top rated hostel in Paris here on the site, has 300 beds, and is at least showing some availability in various dorms over the coming days. Availability for booking engines is always limited, so the numbers reported here on the site aren't a good guide, but calling them might be worth a try. And if not them, then try going down the list...
[ Edit: Edited on 21-Jul-2009, at 14:32 by Sander ]