My neighbor, is a retired DreamWorks Generalist who started working there when they were founded.
He told me whenever they were cutting people, they would keep all the programmers, the top 40 ish% of people that work on one task (lighting, rigging, modeling) and 70 ish % of the generalists.
Basically he says if you want to keep a job for a while, start as a generalist, and know how to code. He said it basicly like this. If you are a generalist, and they don't have any room in the department you want to work in, they can still hire you as something else, and once you are in, it's only a matter of time until you can transfer to another part of the pipeline that you want to work in. Also if they are cutting people, being able to do more then one thing decently will make you more valuable to the company.