I just saw Deep Impact on video and once again noticed an interesting technical point. (This is unlike Armageddon, which had no technical points.)
They use an Orion Drive to power the spaceship sent out to destroy the Asteroid. This is exactly what you would use. Naturally they depicted it as a clean beam of light comming from the back of the spaceship, and not what it actually was, a series of small nuclear explosions being set off behind a big lump of steel to push it along. This would be much messier, harder to show in special effects, and would probably require some technical explanation, which would not do.
Still, if you absolutely had to get an interplanetary spaceship up and running in the smallest time possible, using current technology, that's what you'd use.
Studies in the 1950s showed that, using 1950s technology, an Orion drive spaceship could reach 2-10% of the speed of light. Modern technology should do much better than that.
Using the same basic design, modern materials should be able to halve the weight of the steel design. And the nuclear bombs they had probably had a weight/power ratio of at least 10 times our modern micro nukes.
So given that the fuel (nuclear bombs) was 50% of the total weight, that gives a modern ship with a total mass of about 30% of the original, for the same thrust. Because the weight advantage will be reduced as the fuel is used up, the end result would not be 3 times as fast, but it would be a very nifty interplanetary machine.
Of course the antinukers would go off their heads.