Maybe I'm just a dreamer but it seems like it's not such an impossibility.
I think most people do as well, at least on an un-conscious level. Even if it's often depicted in movies for a feel good effect, after major catastrophes people discard all the worthless walls between us and help others. Even those who seem to be cruel or uncaring by leaving or saving themselves are usually too scared to think properly in the first place.
There always exists the possibility that we don't survive, there are always plenty of ways according to the news. But the human spirit of survival is very strong. If anything we have ever known will survive it would be us. Not a cockroach.