UPDATE 2/07: Even though this post is now several years old, I noticed it still comes up second on a google search for my department. Thus I’m writing an update.
OK, so we are a little behind the times in having this disciplinary conflict. Ostensibly it is a conflict between literature and writing, or at least it has devolved into that. I believe this is a misunderstanding that has been perpetrated by the discipline as a whole. I see it instead as a conflict between those who maintain a bourgeois, hegemonic system of language and cultural values and those who take a critical and at least progressive or reformist, if not revolutionary or experimental view, of language and culture.
Those in the former, though typically literary studies specialists, may continue to proclaim the importance of writing; it is simply that by "writing" they mean grammatical correctness and the performance of certain stylistic conventions. They uphold traditional, canonical views of literature, including a strict limitation of interpretation within the bounds of new criticism. They tend to be luddites and to reject "postmodern" theory as absurd. Generally they teach in a lecture driven mode.
Those who are in graduate school, at least the less cynical of you, may find it surprising that such faculty continue to exist in large numbers across the nation. And no, they are not simply older faculty nearing retirement.
The latter group represent a cross-section of English Studies, though in my experience particularly in rhetoric. One of the most misleading elements of the literature/writing binary is the role of "theory." Conventionally rhet/comp people have stuck by their pragmatism in rejecting theory; theory has been claimed by literary scholars at elite institutions, while many of their colleagues at other schools have not embraced it. I think the result has been that many rhet/comp people have come to see theory as something that elitist literary scholars do, something that is quite impractical from a rhet/comp view, and of little worth.
However, I think there are a growing number of rhetoricians who do not see things this way. In part we have cultural studies to thank for this. We also have to recognize the important role cultural studies of technology and new media studies has played and might play in the future in bringing a powerful understanding of the roles theory might play in teaching and researching writing.
In any case, the latter group is not just "writing" faculty. It is teachers of experimental and noncanonical literatures, media studies, cultural studies, and so on. In other words, it is the folks pushing in many directions on the aging boundaries of traditional English Studies.
This is the conflict that my department now faces: one where we must decide how we are going to move into the future.