I think you mean the "biosphere" rather than "we". Modern humans have existed anywhere from 50k-200k years. Just to put the time scales into context.
EDIT: Just to clarify: As long as disasters happen slowly enough and there are actually local maxima for the species to evolve "into", everything may be fine for "humans"... but those assumptions may be overly optimistic.
EDIT: Just to clarify: As long as disasters happen slowly enough and there are actually local maxima for the species to evolve "into", everything may be fine for "humans"... but those assumptions may be overly optimistic.