The skies would fill with dust, and darkness would settle upon Earth. But once would be enough.
Smaller impacts are much more common, although their effects are far less dramatic.
Hills, of the Los Alamos National Laboratory in New Mexico, has for seven years been using computer simulations to study the potential effects of collisions with comets, asteroids, and assorted cosmic debris. Hills has little doubt that cosmic collisions could change the course of civilization, as paleoecologist Mike Baillie argues. The problem, in Hills' view, is that impacts by asteroids or comet fragments big enough to cause years of environmental disaster are relatively rare on a human time scale. But to have four in that time - I would be rather skeptical. Baillie finds evidence in tree-ring analyses for three to five periods of ecological upheaval in the past 4,500 years.