Given their approach to Apophis, I have to wonder.
I think the latest issue of Popular Mechanics had some good information on this. That said, the answer is really simple. We build a variant of NEAR-Shoemaker. The NEAR-Shoemaker probe successfully landed on an asteroid and remained in contact for 17 days. That is more than enough time for what we need it to do.
You see, in this case, we can modify the baseline NEAR-Shoemaker with a physics package from one of DOD's special stores. Land the probe on the asteroid, activate the physics package, and the problem should be solved. And we have plenty of time. We just need to get off our butts and do it.
Or do we want to get hit?