I believe there were so far three Extinction Events in Earth's past. I think one of them pretty much wiped out 95% of all life on the planet. And yet, as you say, life bounced back. I would however, attribute that more to the incredible resilience of life itself, than to being favoured by something or someone.
As for the asteroid impact, there are many shows on Discovery, and some tend to be a little... flamoyant. As far as I know, the Extinction Event caused by the asteroid impact was not something which happened overnight. It was a rather long process in fact... paleonthologists can confirm that as they know that not all dinosaurs died off at the same time. In different part of the world the extinction happened at different rate.
What probably happened (because no one knows for sure and its all speculation) is that the impact threw up so much fine dust into the atmosphere that it crated an aerosol layer which blocked out a large percentage of Sun's radiation from reaching the surface - something simmilar is predicted to happen if there ever is a widespread nuclear war, and a simmilar effect caused a "mini ice age" when Krakatau exploded (the famous year-long winter which was felt around the world).
However, this effect does not last just one year - it lasts long enough to trigger an Ice Age! What happens is that Earth falls into a sort of a feedback loop. Lowered temperatures caused by the dust cloud cover cause the buildup of polar icecaps beyond a critical level needed to alter the planet's albedo - the amount of energy reflected back into space increases because the ice and snow cover are white and absorb far less energy than darker oceans and landmasses. This in turn lowers the temperatures even further until a new equillibrium is found.
Dinosaurs, dependant on abundant plantlife which can no longer survive the altered climate, start to die of. First to suffer are of course plants. Herbivore populations start to drop because those giant reptiles need a massive amount of food daily to keep going. Naturally, carnivores soon follow.
Who survives? The underdogs of the food chain - mammals and small critters (compared to dinosaurs) who can survive on much less than the giants now dying across the world. Mammals are also far better equipped to deal with a cold climate. Size ceases to be an advantage and becomes a death sentence.
Fish and marine life of course survive as well, largely protected because even during an Ice Age there are plenty of oceans to swim in.
As for oxygen, keep in mind most of our oxygen actually comes from the oceans, from the phytoplankton. It needs sunlight much as other plantlife does for photosynthesis, but since I dount the world was scolded in blistering air during the impact, I think much of the plantlife survived in the tropical regions, where the most oxygen producing forests still are (for the time being).
In the end, I don't think we humans can permanently damage this planet or render it uninhabitable yet. We can kill ourselves off, yes, but life itself is just too tough. If it can exist in an oxygen-free environment at temperatures of several hundred degrees Celsius and produce complex life forms such as worms and crabs, then it can survive anything we can throw at it as is.