I believe humanity will survive, but at a significant cost to lifestyle (at least from the point of view of this American). I'll miss the places that are beaches right now being beaches, and I'm not looking forward to the economic disruption as food sources change.

We're an advanced enough society that in a nightmare scenario, we could pretty much weather several generations in a cave under a tightly-controlled resource regiment. But not seven billion of us, and I don't look forward to the culling that would happen as a result of massive climate upheaval.