I doubt that it goes that far, we humans are a bunch of tough motherfrakkers. What worries me is that overpopulation and climate change lead to a good old-fashioned conflict about land. Add resource depletion to it and some nasty wars seem like the most natural consequence.
So I think that not we as creatures are in danger but our civilization. And being a bit of a conservative Hobbit I would rather have things stay the way they are, with some minor changes, than face an unknown new form of living together.
Being German I am perhaps more sensitive to this. You guys had FDR who basically saved capitalism via the New Deal (the above mentioned minor change) whereas we guys had no such thing, skyrocketing unemployment and then the nazis came.
So yeah, I'd rather have us try to do some moderate things to slow down the heating of our place than risk our societies.