How far away can we see a cataclysmic asteroid?

this is for research purposes. how far away can astrologists detect an asteriod headed for earth? 1 year, 2 years, 5 years? I'm talking about an asteroid that can cause the end of the world - so one that is one or two miles big. Can that sort of asteroid be 1 year away and *not* be dectected (i dont think so but i'll ask)