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The tactical missle would probably work as long as the object was an asteroid and you didn't break it apart when you detonated the warhead. The real problem comes if the object is a comet. From what I understand, the consensus on a potential comet strike is "bend over and kiss your ass goodbye" since a thermonuclear explosion would most likely either shatter it or just be absorbed by the ice/snow/fluff. If we had say 5 years warning, I think that we have the technology to at least try the detonation theory since we could haul a warhead up pretty easily on either an Atlas or a Russian lifting body and then mate it with a solid fuel booster of some sort to sling it out. It would be incredibly dangerous since we're talking about moving a pretty significant amount of plutonium (a lot more than the 14 oz that the Pluto mission had on board), and if something went wrong that part of the Earth is uninhabitable for the next 100,000 year. Then again, it might be a moot point with a large enough comet or asteroid strike. But if whatever it is happens to be 5 days away, well, start working on the flexibility in your back so that you'll be able to reach your ass.
Then again, you could just send Bruce Willis and Ben Affleck out on a modified space shuttle with an Aerosmith soundtrack and have them save the world at the last minute. That's what I'd do.
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