Nuking large objects in space is useless. All it would do is turn a giant bullet into a giant scattershot shotgun blast. Same effect on earth.
...not really.
When you crack an asteroid to small pieces you dramatically increase the amount of surface exposed to atmospheric heating. This equalt to more of the asteroid vaporized during entry, which causes less of the asteroid to actually impact the surface, and as it's the surface impact that causes most of the damage (although atmospheric explosions à la Tunguska can also do significant amount of damage), shattering an asteroid early enough could very well be rather helpful.
In short words - a one cubic kilometre asteroid would plunge through the atmosphere with great ease, impact the surface and wreack havoc on at least one hemisphere (guesstimate), but one trillion stones of one cubic metre would all burn in the atmosphere, provided that they were spread to big enough area.
Physically, the impulse would be the same and energy released would be the same, but distributed on wider area and in longer time. It's not the energy that kills but the time in which it is released.
Shotgun is only effective at short range compared to a rifle...
Anyway, even at worst-case scenario... 880 megatons is not that bad globally... Well, it's about four times the Krakatoa explosion, but the effects of impact would be greatly related to where it would hit.
Meh, it's gonna be cool whatever happens. The way I see it, I'm going to survive my life whatever I do. Until I die. Which will eventually happen even without asteroids impacting the planet, so... what gives. AT least that'll be a kick ass way to plunge the world to post-apocalyptic nomadic tribal culture where survivors try to live in frozen cities, crawling with man-eating, infectous zombies and other nice phenomena...