Nuclear bombs are overrated as mechanisms to steer asteroids around. To do this effectively would require a thorough analysis of the asteriod's structure and composition, which could only be done by complex on-site probes. The "cleaving" of the asteroid in "Armageddon" by a buried nuke was wishful fantasy.

A nuke set off on a frangible (chondrite-type?) asteroid or a comet nucleus would just break it into a bunch of nasty little chunks that, in close formation, would cause almost as much damage as the original asteroid.

The only really effective way to steer an asteroid is to deliver something on site that can "dock" with the asteroid and provide controlled thrust. A nuclear-powered mass driver, capable of "mining" the asteroid for reaction mass, would be ideal. Unfortunately, developing something like this would be orders of magnitude more difficult and expensive than a simple warhead delivery system, and, barring new wonders of automation, may even require a manned presence to work properly.

The good news: such a system has many more uses than diverting nasty earth-colliders. Such a system could be used to mine asteroids on site, using the mass driver to fire ore payloads back to some near-Earth location for processing. Or, it could steer the whole asteroid with great precision into closer orbits (not too close--a lunar Lagrangian Point maybe) for easy mining access by other methods.

This benefit would certainly make up for a lot of upfront costs, and if no asteroid ever came on a collision course with Earth, the mass-driver system would not go to waste.