I've been speaking very broadly, as much in terms of definitions as processes. What do we mean when we speak of consciousness? Take it back to Descarte's cogito: I think, therefore I am. It's a statement of self-referential information processing.
To exist as a conscious entity - Nagel's be-able thing of What is it Like to Be a Bat? - is to think, at some level, about one's own thoughts.
Self-reference.
Since that's how we define consciousness, it's little surprise that when we look at conscious processes, we do indeed find self-referential processing.
Hofstadter of course covers this with great thoroughness in GEB, which is why I keep exhorting Nick to read it.