The idea being worked with is some kind of a solar-sail, which would divert the asteroid away. I don't understand why the heck they just simply don't:
1 Nook the thing out of the path.
2 Nook the thing down to dust.
The asteroid (or pile of rocks rather) is less than a qurtermile x quartermile. The fireball of the biggest H-bomb detonated was 5 miles across.