Well before I get to NASA's actual plan, I first want to describe an upcoming project NASA is planning that will hopefully lead to a better understanding of asteroids and their place in our solar system. The project is called ARM or Asteroid Redirect Mission. Its purpose is to locate a small asteroid close enough to Earth and to redirect it so that it will safely orbit our moon. this will then let NASA astronauts go on a mission to analyze many factors behind the asteroid such as its chemical composition and topographical features. This will further our understanding of asteroids in our solar system and how to deal with them.
With that being said, NASA was called upon by Congress in 2005 to present defense plans against an incoming asteroid. After two years of research (because of such a reduced budget), they returned to present their plans to Congress. They presented four plans that worked best for different asteroids, but argued that the most reasonable and most effective plan is to detonate a series of "standoff" nuclear blasts. This means that nuclear bombs would be sent near the surface of the asteroid and detonate close enough to push the asteroid off course little by little. NASA scientists agreed that having the bomb on the surface or beneath the surface would create smaller chunks of asteroid with unpredictable trajectories. Having a series of nuclear bombs detonate near the asteroid would push the asteroid into a different trajectory with every blast. Below, I have drawn a diagram of what this would look like. the dotted line would be the original course of the asteroid, the small asterisks would be nuclear explosions near the asteroid, and the solid line would be the resultant course of the asteroid after the detonations.
Through the series of nuclear detonations, The course of the asteroid would slowly be altered. After enough explosions, the course would change enough to miss the Earth entirely. By having the nuclear bomb detonate near the asteroid, and not on the surface, you lessen the risk of pieces of the asteroid breaking off and entering the Earth's atmosphere.
All we can hope for is that NASA uses astrophysicists and make them learn about nuclear explosions, and not use nuclear technicians and make them learn astrophysics, or better yet... have both of them work together to save the planet...