How could they? Anyone looking up at the sky would see the comet MONTHS before it hit! The tail of such a comet would extend half way across the sky and be brighter than the Full Moon! Anyone looking up at the sky would SENSE that something is in the offing! It is physically impossible for a comet to sneak up on the Earth and blast it. Its tail would give it away long before the event happens.
Now, having said that, asteroids are a different matter. You would not necessarily see a big asteroid until it was a week or less away from impact, and then only if some amateur astronomer had happened to spot it.
Sweet dreams!