Couldn't we just nuke them?
The other problem is that if you blow up an incoming asteroid, then instead of a single body hitting the Earth you have hundreds of smaller bodies hitting the Earth.
Try this in Universe Sandbox...
- Open up Earth & Moon
- Select "Asteroid" from the preset list under New Bodies
- Shoot an asteroid at the Earth
- Right click on the asteroid
- Set the explode value to 1 km/s (you may want to experiment with different values)
- and then click "Explode"