For an asteroid or a comet in a highly eccentric orbit, it will be travelling faster as it nears the Sun (perihelion), and much slower when it is far away from the Sun (aphelion). A given rocket might provide the same thrust, and therefore impart the same change in velocity (delta-V) to the asteroid regardless of where it is. So the delta-V would have more effect when the asteroid is moving slower, since it is a larger percentage of the orbital speed. Therefore it is most economical to intercept and push the asteroid when it is at aphelion than at any other time during its orbit. If the asteroid is at or near aphelion for several years then their idea might be useful. But if the asteroid is there for only a few months, then a more decisive push might be in order. In terms of Earth impactors I don't think we'll get much warning, if any.