If we find it's likely to hit, THEN we need to send up a mission of some sort ASAP: the earlier we start diverting it, the easier the job will be. You do NOT want to blow it up without changing the orbit: that just changes it from getting hit by a cannonball to getting hit by a shotgun blast, so to speak. Think about the NYC scenes from "Armageddon", on a worldwide basis. . .
Stay well - Stay safe - Stay armed - Yorktown
Plus, assuming NASA determines a high probability of a hit by a single big object, wouldn't blowing the object into pieces tend to spread the object out, making it likely that many of the pieces would miss Earth--that is, only the pieces in the center of the swarm (assuming the initial rock is dead on and assuming the orbit of the entire swarm is not changed) would hit. That rock is going to go a long way in 17 years and the swarm would have a long time to spread out.
Since you seem to know whereof you speak, one more question. Would our largest nuclear bombs have enough energy to nudge the rock enough or to break it into pieces? A lot of a nuclear explosion in space is just going to disappate in the wrong direction. In fact, since the nuclear weapon would not actually throw a subsantial amount of mass at the object, how would energy transfer to the object. Of course it would throw a lot of subatomic particles at the asteroid; but how much energy could be transmitted in that manner.
Sorry about the barrage of questions. This could be a very serious matter and I am curious.