Nuking an asteroid might not work
I could have told them this.
The right way to deal with asteroids is to set up a system to detect and track them as far away as possible, and use something that sets up a gentle, constant push to change its course. The farther away you start, the less of a push you need.
Of course, you need VERY precise tracking to predict a trajectory way out in space. A program to drop microtransponders on the most likely Earth-crossing suspects would be a good start.