NASA's proposals are just at the initial stages, and the spacecraft needed to send an astronaut that far into space doesn't even exist yet. But, with a smallish asteroid called Apophis having already been identified as a possible threat to Earth in 2036, NASA is taking the exercise very seriously.
Chris McKay of the NASA Johnson Space Center in Houston recently said "There's a lot of public resonance with the notion that NASA ought to be doing something about killer asteroids ... to be able to send serious equipment to an asteroid. The public wants us to have mastered the problem of dealing with asteroids. So being able to have astronauts go out there and sort of poke one with a stick would be scientifically valuable as well as demonstrate human capabilities."
It is estimated that an asteroid weighing one billion tons and with a diameter of just one kilometer could generate the equivalent of a 50,000 megaton thermonuclear explosion if it hit the earth at a 45-degree angle. Attempts to break up such a large object with an atomic warhead may serve to only turn one large problem into thousands of smaller problems, so scientists agree the best approach -- with enough warning -- is to gently nudge the object into a safer orbit.
Mirrors, lights and even paint could change the way an asteroid or similar object could absorb enough light and heat to shift its direction over 20 years or so. Mankind could be forced to take more drastic measures with less notice than two decades. Such measures would include setting off a massive explosion on or near the object to change its course. NASA's Deep Impact mission tested a different technique when it placed an object into the path of a comet and forced a collision in 2005.