Waiting until after the "2012 prediction" is behind us would be best. It seems most people can't incorporate both the Mayan End of Days and climate change into their future plans and goals, so adding a third 'hoaxable' problem to Earth's future won't help.
With that said, I can see society accepting a killer asteroid over climate change - since the science for the latter is more abstract than "hey look at this asteroid coming right at us."
End of the World movies and books are overdone, so there wouldn't be a need to break the ice to the public through popular media. I think it would be safe to simply state the danger directly.
It seems fear would drive some people to insane things, but enough people to be driven to help the situation, ie. agreeing to help fund, through taxes, research and operation of a mission to divert a killer asteroid.
LessWrong is not big on discussion of non-AI existential risks. But Neil deGrasse Tyson notes killer asteroids not just as a generic problem, but as a specific one, naming Apophis as an imminent hazard.
So treat this as your exercise for today: what are the numbers, what is the risk, what are the costs, what actions are appropriate? Assume your answers need to work in the context of a society that's responded to the notion of anthropogenic climate change with almost nothing but blue vs. green politics.