Do it. Send them as much material as you can. Just look at the situation like this: by beign waitlisted, you are basically rejected by the school. True, there is a small chance that you may get accepted in there, but that is a very slim chance indeed. Thus, you really don't have anything to lose by sending them whatever you can. This is a much better action to take then simply not do anything to improve your chances.
Look at my case. Back in February, Penn sent me an e-mail stating that its admissions committee really liked my file, however, they wanted to review other applications before making a final decision. They did invite me to send them more documents: "for example, one letter of reccomandation, one additional essay, or one updated resume." Well, I paid close attention to the word "example," so I sent then 3 additional letters of recommendation by professors, two letters of recommendation by my supervisors at the organizations i volunteered with, and two additional writing samples of papers I had written while pursuing my BA. I think that is the reason for why I am still under consideration, instead of being waitlisted.
Once again, you don't have anything to lose, so just do whatever you can to get out if this situation. If you have a good relationship with your professors, they will certainly try to help you and write a letter, even if you ask them to have that ready for let's say... four days.