I know this is a fault of the movie, not the paper, but there aren't any asteroids 1000 km in diameter (Ceres is just a little bit smaller).
The only way that the movie could be even remotely plausible would be if this were an extra-solar body coming from interstellar space. Otherwise it would have been detected centuries ago. (Actually, I think the movie indicated something like this). It would also probably be traveling at a high rate of speed since it would have been dropped almost all the way down the Sun's gravity well.
Still, such a large object would have likely been detected months, if not years (decades)? before impact; even it it were coal black. (I believe the large nightly deep sky surveys would've caught it way in advance). Astronomers have recently been finding much smaller objects way beyond the orbit of Pluto; even if headed directly headed to earth they would take more than a century to get here. But since that would've allowed NASA to train its astronauts how to use the drilling gear used by Bruce Willis et al. the writers made the time very short (I think it was 14 days).
Far more likely would be the scenario in "Deep Impact" a much more scientifically accurate (boring?) movie. Here the asteroid was only about 10 km or so in diameter, or less than a millionth the size (volume, mass) of the one in "Armageddon". Also, I think, they intercepted it deeper in space and were just trying to deflect it, so a realistically sized nuke would have been able to do the job. And they carried more than one! (So no super heroics requiring Bruce to stay behind).
Obviously the size and speed of the asteroid in "Armageddon" was only to impress the audience; "Texas-sized is a lot more awesome than "Manhattan-sized". (Both would've been "ELE"- Extinction Level Events). The only possible way any realistically sized nuke (remember, those 1950s super H-Bombs were BIG, I don't think the very largest could be carried by plane), could do the job described in the film would be if the asteroid was shaped like a bow tie and the bomb placed in the fragile center (yes underground would also be important). Oh, and it should be (rapidly?) spinning to counteract its own self-gravity so that it would fly apart (and also perhaps be structurally weaker).**
I seem to remember there being something in the movie about it being shaped like this (not spinning though). The writers evidently sought to make their story just a little more plausible by adding even more implausibility to it. So what else is new (in Hollywood)?
*I don't know if any of the recently found Kuiper belt objects are larger, Ceres was the largest asteroid listed in Wikipedia.
** Actually, if the asteroid WAS in some sort of bow-tie or dumbbell kind of shape, it MUST have been spinning. Otherwise it would've collapsed under its own weight into a (rough) sphere.