I would think that given the opportunity some governments who have the power to do so might contemplate changing their course in order to control where they hit. What an interesting idea for a novel/film...sigh if only i was a writer
I believe the current prescription for asteriods aimed at the Earth is to deflect them. Talks of exploding nuclear bombs on them seems to be too hazardous.
Searching for asteroids less than 1km across, hey? Surely there's a way of using some form of radio or laser equipment for an asteroid radar? Seems more effective than just looking with a big camera.
Destroy them? Possibly. Detect them in time and you can paint them. It's known as the Yarkovsky effect. The change in radiation absorbed/reflected, subtlely alters the the asteroids trajectory.
they reckon the asteroid that hit Mexico millennia ago was about 6 miles across. The crater it left is about 200 miles across. These things hit very hard. Fortunately, we have Bruce Willis