They need to be massive enough to do some real damage, and this will require a lot of energy and luck to divert as there is a low chance you'll find a few hundred on such a trajectory.
Just getting the ships in position to shift their orbits will take weeks to months. Meanwhile, nukes already hit. You'd only need 100km/s of delta-v, which is very doable at those timescales with a sub-ton payload.
