Is this deli meat in your refrigerator at home? Was it slimey when you bought it? If not, the slime is caused by bacteria growing on the surface of the meat. Toss it. (And if it was slimey when you bought it, there is a chance it was stored improperly at some point and was going bad when you bought it).
If the meat your slices were cut from is overprocessed turkey-like meat-and-water-product garbage, that may also be why you are seeing this. Make sure you buy from a decent piece of meat.
I'm not sure what turkey standards are, but I know that for ham, the USDA requires certain labeling depending on how much water has been added to the product. The more water, the more processed and lower-quality the meat is.
Grades are:
1. Ham.
2. Ham in Natural Juices.
3. Ham, Water Added.
4. Ham and Water Product.
Turkey probably has a similar grading system.
I wouldn't go below 2.