Yeah, I had to ask two profs who didn't know me well. I had better reqs, but some schools specifically ask for letters from profs that "taught you formally", ie not profs you TA's for, did research with, etc.
What I did was go over in my mind what profs might actually remember me from their huge classes. Did we ever chat in the halls? Maybe they stopped by the lab and we chatted there? you get the idea. Anyhoo, I sent out nice formal emails to the profs that made "the cut", explaining who I was and asking for an appointment so we could sit down and talk. I also described myself briefly, so hopefully they could place a face with my name! Much to my suprise, every prof I contacted responded promptly, and agreed to meet with me right away (and most said they knew exactly who I was! man, some of these guys/girls have AWESOME memories...)
I prepared bound packets for each prof. Within the packets were a copy of my transcript, a copy of my AMCAS, a CV, a more inclusive list of activities, and a short list of references. My advice to you is to prepare packets!! The profs were really appreciative and impressed.
All the meetings I set up went great, and in the end I got to pick and choose which letters I sent out to back up my "real" recs (the ones from people who really knew me).
So the take home message here is that it IS possible to get good recs from people who don't know you well. Just be polite and professional, and go the extra mile to provide them with all the info they might need.
Oh, and send thak you notes/emails, and let them know how it turns out for you!
Good Luck!
Racergirl