At UMCP, they have a program called Gemstone that I was in for ~2 years; the idea was to take a group of >10 undergraduates and have them complete a real research project over the course of 4 years. Apparently, they've learned from their high attrition rate and now try to ward away bad matches.

They didn't have the size problem- many projects were too big, and got seriously scaled down. The same interpersonal issues were present; the same priority problems were present. Having too little work may be a sufficient condition, but it's by no means necessary.