I would never suggest to use nukes to blow up an asteroid. If you did now you have thousands of smaller pieces that can fall to earth and cause damage not to mention the radioactive fallout. Instead, and as mentioned in your quote,
BOYCE: He says most asteroids could be deflected with something like a gentle push from a rocket.
Rep. ROHRABACHER: We should be able to spend hundreds of millions of dollars in order to protect us from an asteroid or a comet that would do far more damage than the terrorists could ever imagine.
As I understand it, the idea is to land on an asteroid or comet with some sort of thrusters that would be used to nudge the neo off of its collision course with earth. If we don't conduct tests landing on these objects we won't know what types of anchor systems would be needed for the thrusters. I am no expert but to me that sounds feasible and makes a whole lot more sense that nuking them.