The best campaign I can think of is an advertisement of an asteroid hitting the earth and the slogan "If only we'd seen it coming!"
Not everyone is interested in space but nearly all of us have a sense of self preservation. A large impact may be unlikely but it only has to happen once to end the entire human race. The movies 'Deep Impact' and 'Armageddon' promoted a lot of public debate. I think a campaign detailing recent near misses and how much money would be needed for new telescopes to find and track NEO's could be one way of getting some attention. People love that sort of apocalyptic stuff.