^^^Given how much more and better technology we have now, a real "dinosaur killer" object would probably be seen from a ways off, yeah. And unlike the premise of "Armageddon", there are so many observatories, deep-space radar installations and satellites that no single organization could keep the news from breaking.
But the end would be pretty swift, at least for the "higher" organisms. What with an ocean impact raising miles-high waves, triggered earthquakes, red-hot secondary debris eventually falling over pretty much the entire globe and the resulting atmospheric dust causing a new ice age when the impact energy dissipated... Life might be reduced to the microbial level, leaving multicellular organisms to evolve independently a second time.
Maybe lichens, algae and such would make it. And cockroaches.