I don't know what it is, but I don't think it is fat or bacteria. Why fat? Deli meat is lean and how/why could the fat get out of the meat to form a slime? Also slime isn't fat. The fat in meat is mosty saturated at room temp and is a solid.
Usually it is fat. Fat gels, even the slightest bit from meat. The cold, and the opening and closing of the refrigerator allowing for hotter air to move into colder air constantly also lends to the gelling process of fat. If you want to see the gelling process for yourself, take some EFA capsules and stick them in the fridge. They'll congeal and form a kind of lump of slimy looking crap inside the capsule. I had a guy try to return some CLA's once because of this. He said they "went bad" and showed them to me. They looked like little capsules full of grease. I asked him if he put them in the fridge. He said he did and then said he has always done this and they never did that before. I hate liars.
It could also be bacteria, because of the hot-air/cold-air thing. Like if you ever leave steak in the fridge you'll see after a while it starts to get white blotches and fuzz on it just like fruit. There's some cultures of bacteria that will grow just about anywhere with the right temperature fluctuations. And one thing I noticed is the leaner the meat the faster it goes bad. I buy Boar's Head Turkey, which is the best turkey I've ever had, but the shit spoils faster than a set of rims gets stolen at a Puff Daddy concert.