One perspective is that human population and various other characteristics of the economy & environment roughly agree with the "Limits to Growth" standard run modelling that was done 40 years ago:
I am not sure if "doomed" is the right word. It seems pretty plausible that existing civilisation will collapse, as many human civilisations have done in the past, and there will be additional human suffering (more than the considerable amount there is now), but I doubt we as a species will become extinct within the next few hundred years.
http://cl.ly/image/3H1A3S341k1t
Of course, we might muck it up good in a few short years here.
Edit: who on Earth decided this was a good comment to downvote? We are doomed.