The first issue with Jaynes' thesis is that you probably haven't really ever thought about what consciousness is. When you do, it is hard to pin down:
And the privacy of it all! A secret theater of speechless monologue and prevenient counsel, an invisible mansion of all moods, musings, and mysteries, an infinite resort of disappointments and discoveries. A whole kingdom where each of us reigns reclusively alone, questions what we will, commanding what we can. A hidden hermitage where we may study out the troubled book of what we have done and yet may do. An introcosm that is more myself than anything I can find in a mirror. [pg. 2]
I mean ... really ... what is that voice? We say and feel that it is in our head, and we know that physically it is, but how can that be?
And, if you think about it, that voice has never had any interaction whatsoever with another voice like it - unless you have schizophrenia.
And yet ... that voice is who you think of as ... me.