This was discussed in another question related to reaching earth's core using nukes. I re-ask it here to (1) stop unintentionally hijacking other topics, and (2) be able to respond (as someone cut my newbie score from 50 to 49).
My position, to be clear, is that it might be possible (depending on the scale of things) but is highly improbable today, despite the landing of a small unmanned craft on such a celestial body. I stress that point since either long-term contact or penetration of such a body would seem to be a must, given the fact that a nuke does little in the vacuum of space other than produce enormous light, heat, EMP and other forms of EM radiation for the briefest instant. Landing and anchoring a robot capable of drilling into an object possibly made up largely of iron would be a far cry from anything that's been done.
Surely one giant step has been taken. Further, a small nuclear reactor (Rover) has been successfully deposited on Mars. But the details of a mission that cannot fail have to be ironed out. I have a good deal of experience with defense projects, and while most are remarkably successful, they are also remarkably time and effort consuming, including very long test phases. Asteroid test environments aren't easy to come by.
So (a) could it be done at all, (b) if so, what stages of reasonable development effort would have to be met, and (c) how long would a concentrated effort to produce something with likelihood of success take?