[AntonioXYZ]

Because asteroids are all different sizes, have different density, and are made of different substances (we know this thanks to space exploration) some methods work better than others, depending on the asteroid. A nuke blown up next to a asteroid that is a loosely bound pile of rubble might make things worse, sending many different sized meteors toward the earth over a wider target. For icy asteroids, one proposal I found interesting is directing concentrated beams of sunlight to a point on its surface. As it heats up, it’ll spew a plume of debris, essentially like a comet, or rocket. Given enough time that might help change its course.

As for NASA's budget, here's what the Planetary Society's position is:

After reviewing the budget, we believe the new plan encouraging government, private, and international partnerships will allow humans to go back to and beyond the Moon faster and more realistically. We also were heartened by the strong support to Earth and space science in the new budget, including the authorization to re-fly the Orbiting Carbon Observatory and the full funding of the robotic Mars program. We will be calling on Members of The Planetary Society to urge Congress to support and appropriate the necessary funds for the new plan.

http://www.planetary.org/blog/article/00002328/