To the disdain of many, I'm back

While the remnants of a nuclear explosion might not have much mass in itself, that's not the whole story. If you remember back to high school physics, you'll remember the equation f=ma. A nuclear explosion emits lots of particles, and while they may not weigh much initially, they are travelling extremely fast. In the vicinity of 100,000 times faster than that asteroid.
High intensity particles aren't the only constituent of a nuke, nor are they even the main constituent. The energy released in the form of photons, although not weighing much, still possesses momentum. If this were another time, I'd probably calculate the energy contained in both the rock and nukes and see what would be needed - I'm sure someone else in here is knowledgeable enough to do so (and check that this post makes sense in the first place...).
Unfortunately, using regular nukes won't have much of an effect. When a bomb explodes, its power is radiated in all directions, meaning its overall effectiveness is cut down to a fraction of what it really is. Also, certain types of asteroid can soak up such a blast, distributing it throughout its structure in a way that makes the initial blast pointless.
In this case, you'd want to use hundreds, if not thousands of warheads, to deflect it. And in that case, some hot-headed people would probably just say "blow the ***** up!" and hope that it's blown to bits small enough that they burn up in Earth's atmosphere (I guess you could meet halfway, blow up the rock into small chunks, then deflect those with the rest of the nukes). Beforehand, you'd probably want to listen to all the scientists and geeks and asylum inmates to see what whacky ideas they have. Most ideas involve either attaching something to it and towing/blowing it away, or blowing up a small part of it to make the rest shift direction. Either way, only a small change is needed
In any case, it's not as simple an issue as I may have implied in my first post.