BBC's UKTV documentary arm's Killer Asteroids: Averting Armageddon tries to shed some light on just that - an asteroid over a kilometer wide hitting the Earth's surface and exterminating life as we currently understand it. Despite our best efforts to catalogue the skies above, only a relatively microscopic portion of them have been "checked" for this type of killer comet.
Despite our limited surveying capabilities, we have been able to detect an asteroid that is on a collision course with our planet, due to hit around 875 years from now. This discovery has led to a number of astrophysicists scrambling to find a way to avert what is widely accepted as our definitive demise, unless of course these scientists succeed.
Initial hypotheses posed a solution that is basically the story told in Michael Bay's 1999 blockbuster film Armageddon, where a nuclear warhead would either be fired at the meteor or taken up to the asteroid's surface and buried deep within its core prior to detonation, with the intent of blowing it apart before it poses a threat. Scientists almost immediately discredited the idea, as nuclear weaponry we currently have at our disposal does not even come close to the caliber necessary to accomplish this.
Nuclear warheads in use today have the capabilities in the 20 megaton range, whereas we would need around a 1000 megaton explosion to have any effect on an asteroid of this size. And even if this were possible, the dangers of creating a bomb of this magnitude and strapping it to a rocket to send up into space far outweighs that of the asteroid's impact.
A plan B was founded on the basis that a reasonably large explosion created near the asteroid, if it were long enough in advance (ten years is the figure cited in the film) of hitting its target - Earth in this case, it should divert the trajectory of the mass by a few inches. This minute change, multiplied exponentially over the course of the asteroid's travels, would be enough to send it whizzing by our planet at a safe enough distance.
This too is shown to not be a guarantee, and more theories are considered as the film runs its course. Whether any of them are enough to save us one day, only time will tell.