That is a concept that is fairly common in science fiction. A very small nudge on a body very far away will move it enough to be no threat. You can put a solar sail on an asteroid, for example, and over time the course change will be significant. However, on bodies that far away, it is difficult to predict if they are a threat or if we are nudging them into a path that threatens us.
Near term danger is probably the Apollo asteroids because they are known to cross earth's path every so often.