You are correct. The amount of force the rocket can exert on the asteroid is limited
by the mutual gravitational attraction between the rocket and asteroid, and the
requirement that the rocket stay below escape velocity.
This SEVERELY restrincts the amount of force that can be applied. Even if we
deflect the asteroid YEARS in advance; it is going to take some VERY LARGE forces
to deflect asteroids of a size that would be a threat to the Earth.
Dr. Gregory Greenman