Its an interesting question, and one I think is fundamentally impossible to answer; especially without a good definition of what you mean by "singular self-aware consciousness".
In some ways our brains work like this already - our brains are divided up into thousands of paralleled processors which work somewhat independently, but come together to form out minds. I had a link to a video that was a great demo of this - I'll try to dig it up. The text version is: if you give someone a difficult moral question (i.e. putting yourself into danger to save five others), different regions of the brain "fight" to determine what action you take - for example, in the above case the cost-benefit part "argues" with the self-preservation areas of the brain and the social-decision areas of the brain. the outcome of that "fight" determines what action you take.
What that means is when you're stuck with a difficult decision, and experience that feeling of being torn, that feeling is a very real reflection of what is going on between different parts of your brain.
To some extent, a fully singular consciousness (i.e. where individuality is lost in its entirety) is probably impossible, for the simple reason that the "units" making up the group mind need to be aware of themselves to the point where they can care for themselves. Otherwise, a distraction of the singular mind could lead to units starving, or getting hit by cars (or whatever dangers lurk in your world).
In the case of us humans I think this would only be achievable through some sort of mind-machine technology. Our current forms of communication are simply too slow and imprecise to really allow our brains to act together with the degree of coordination to have a functioning "group mind", nor is there a plausible biological mechanism by which our brains can connect in a way which would allow for that to occur naturally. But one could conceive of a mind-machine interface that allows you to connect your brains with the brains of others over the net, allowing you to function much like our own brains do - as a group of separate "processors" linked together into a greater network.
I believe Asimov had a novel based on that later idea...
Bryan
EDIT: as promised, the video I referred to. Its long, but worth watching.
http://www.youtube.com/watch?v=jnXmDaI8IEo&feature=channel
