From what research I've done (a while ago), detection is a very inexpensive project, particularly when measured against many other space projects. Given the technology improvements since I last examined the issue, I'd bet it's even cheaper now.

The effort required to deal with an asteroid is inversely proportional to the lead time one has. Detect a threat ten or twenty years away and you have an easier problem than detecting one a year away. The catch is that the farther out the threat, the less accuracy you have in predicting the likelihood of a collision.

Getting past the detection phase, I proposed designing a small asteroid-landing probe that could be launched when a potential threat is discovered. It would have two functions: tracking (a transmitter on the surface would allow very precise positioning, even without onboard navigation systems) and science (detect the composition and other characteristics of the asteroid). The smaller the probe, the cheaper it would be and the faster it could be delivered.

Ideally, you'd want such trackers on as many NEOs as possible over time, even ones that aren't an imminent problem. Perhaps a large ion vehicle could make a multi-year mission of delivering several of these on a single mission.