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.
Fooling with this until we are dead certain where it is going and what the effects of our meddling would be is not a good idea.
Now, as for the throw-weight of our nukes, I know very little about yields, and I suspect that real detail here is classified. But, at least according to an article I read in Scientific American in the early 1980's, there appears to be such a thing as a "shaped nuke", just like there are shaped charges of conventional explosives. Assuming such IS actually possible, I suspect we'd use that sort of nuke.
As for the energy transfer, the energetic particles of the bomb itself would transfer their energy to the matter of the asteroid, and since it's vacuum on one side, and rock on the other, the explosive vaporization would be on the side of the bomb blast, producing a massive short-term thrust along the rough line of the original blast. It's all Newtonian physics from there (g)