Don't know how well the "airbag" idea would work, but it goes without saying that detonating a nuke against an asteroid is not as safe or as effective as any propulsion method that would apply a precise thrust at a specific point to change its trajectory in a predictable manner.

Most effective but most difficult to develop would be a mass driver system, maybe nuclear powered, that would carve chunks of the asteroid loose and fire them off as reaction mass. It would be difficult to carry enough propellant along to change the trajectory in a meaningful way using conventional rockets, unless one started while the asteroid was so far away that a very tiny push would do the job. And in that case, it would probably be too far away to track effectively. It will be noted that such a mass-driver asteroid propulsion system could very easily be used for mining purposes, but that's another story.

Of course, if we are rushed by something that will hit us in a few years, a nuke hit would at least give us a fighting chance, compared to doing nothing at all.

A good start on this is, of course, cataloging as many asteroids as possible using ground facilities, which could be done for very little (relatively speaking) additional funding. Next step might be to "tag" the most iffy objects with a small ion-engine-powered probe/transponder that would allow extremely accurate tracking, and maybe even be able to analyze the asteroid's structure to see whether or not a nuke would work.