Well, Bergoe, I know a lot of us (me for sure) start out by saying "That depends," so sorry I am doing it again. But it really does depend: on where you are, on what your business is, which businesses you rely upon as customers, lots of things. If you are looking for purely "economic" responses and stats and projections, I don't have them, but I have some other thoughts that are relevant to this topic, from my perspective.
My first reaction to you is that it is a good idea not to take the route of fear. Some people will think "It is easy for you to say that, you are not in my experience," etc. And they are right if they feel that way, because I am not in a bad place right now. I may have different emotions if, in 6 months, I lose my job or if I have to eliminate half my team members; but today I am saying I am not going to operate that way. Where I work, I have a lot to do, and we are in pretty good shape. At the same time, we are looking at ways to make sure we stay that way by reducing unnecessary costs. But we are remembering that we have a lot to offer to people that need us.
So if I am in a better place right now (while others are not), when I say not to operate with fear, that is the best I can do. I felt rotten end of last year, early this year for personally specific reasons, but I picked myself up and out of it by deciding that was not the experience I would accept, and just wore a positive outlook on everything I could do. It was one of the smartest things I ever did, because I let go of a lot of burdens I didn't need. And then had a much experience through the year, and I think I have flourished in a few ways.
I talked about my past personal concerns. The global marketplace is a huge vat of personal concerns that are connected in ways I wouldn't even begin to pretend I can elucidate in an authoritative manner, let alone comprehend. But I think there is something to be said about using some psychology to one's own advantage. I want to keep in mind that I have something to offer and people around me need to be aware of that too. If the economic crisis is like a natural forest fire, then there is a natural series of new life to pick up where the rest left off. We can either give in to the fire or look at ourselves being OK when it is done. I'm going to have a place in my "forest," with other people, after the fire.
How would customer service be affected by crisis that is felt here and there? Well, we are back at "it depends." Some companies might cut their employee costs a lot, so that remaining ones are pressurized to perform in ways they are not accustomed to. Maybe that would result in some stress to an internal customer service group. At the same time, maybe that would create opportunities for that internal service group to shine in new ways. Maybe priority shifts would mean good things for customer service, and a group that used to be seldom recognized now becomes a bunch of stars. Maybe it would be discovered that customer service can actually generate revenue or retain it. On a different note, maybe the need for certain kinds of services would be wiped out and customer service roles would be eliminated.
I think what Johnny said about customer service as an expectation in performance is true, but I also realize that customer service as a function inside a company doesn't exist in a vacuum. It is tied to some other activity that carries a lot of dependencies with it. The opportunity to provide excellence in customer service and never forgetting it is still going to rely on the line of business at a company creating the need for it.
People in various roles would probably want to maximize where they are needed, when you think about the idea of making your presence at a company a worthwhile thing during a time of economic change. In that regard, maybe a customer service spirit will begin to emerge where we didn't think it was possible. :) | 
