If we had the ability to get to the asteroid the power to blow it to bits, we would have the ability to get to the asteroid the power to divert it as well. The hard part would be deciding which path to take. The engineers will always quote an error factor, meaning a planet-killer will likely destroy all sentient life on Earth, but properly placed explosives might divert it to a less hazardous course, and blowing up the asteroid with those same explosives would result in Earth impactors, but they would be survivable, being of smaller size and disbursed over the whole planet.

One-shot decision time:
* the planet-killer might be diverted, thus saving all lives.
* the planet-killer can be blown up, thus saving most lives.

At the moment, of course, this ability does not exist, so we'll all just die,
Dan
--ps--
As for what to save for posterity -- how about me?
;^)