What could be done
As a matter of fact there are many ideas more practical than vague ideas about adapting ICBMs to carry nuclear warheads to, like, "blow shit up". They all require many years advance warning, but as long as the orbits are well characterised we can be fairly sure we'll have it. (The exception is a long-period comet, falling in from the Oort cloud in a hyperbolic orbit; we might do well to get a few months warning for one of those, and their earth-relative velocity is much, much higher than NEOs slowly dawdling around the sun in earth-like orbits. In those circumstances there really would be very little we could do about it.)
Check out the Planetary Society blog reports from the recent Planetary Defense Conference. Includes info about a competition to design a mission to shift the orbit of a NEO called Apophis:
http://www.planetary.org/blog/article/00001922/
http://www.planetary.org/blog/article/00001923/
http://www.planetary.org/blog/article/00001924/
http://www.planetary.org/blog/article/00001926/ and
http://www.planetary.org/blog/article/00001927/
....and earlier posts from a conference on NEOs and law (like, who tells the President? Does the President tell the people? the rest of the world?)
http://www.planetary.org/blog/article/00001913/,
http://www.planetary.org/blog/article/00001919/ and
http://www.planetary.org/blog/article/00001920/
(All published in the last month...)