Hey NASA Redcloak has a question.....
it depends on how quickly you 'need' to do it...that's where the Hollyweird movies like Armageddon get it wrong; they postulate an incoming big rock so close it would have to be deflected in such a short time it would be practically impossible for us to deflect it even with nukes [Sorry Bruce]...but if you are dealing with a rock far enough out that you have plenty of time then even a small nudge would be sufficient to either stop it from hitting Earth or conceivably make it do so eh? less specific impulse but for a much longer time works when the required degree of deflection is much smaller eh?
In which case stationing a mass driver on the asteroid could do it...
Though I think whacking the earth with another dino-killer would be a worse 'cure' than the 'disease' of global warming could ever be...however the same techniques could be used to move a near earth object...say one of the apollo asteroids?...into earth orbit for use as (a) life support resources to support large numbers of people in orbital operations [if a carbonaceous chondrite type] or (b) for metals for orbital industrialization [if a nickel-iron type] or better yet (c) both types for both purposes...and those would then also make a nice counterweight for building a synchronous skyhook [space elevator] as well as the cc typoe supplying the carbon to build the nanotube ribbon from orbit to the surface [nanobot manufactured down to the surface in one continuous piece to get around the recent join strength concerns perhaps?].
I just thought that as long as we're getting into a K-T kinda mood over at NASA, why not go all out?