The 100 megaton example was for a deflection of an asteroid for which we have 18 months of warning. With much larger asteroids we could have significantly more

The 100 megaton example was for a deflection of an asteroid for which we have 18 months of warning. With much larger asteroids we could have significantly more warning time, and so the distance that asteroid would have to be deflected could be much smaller to have it eventually miss the Earth. Other dynamics would probably come in to play too, such as the gravity of other planets in the solar system. Depending on where the asteroid was, where it would be passing through, its mass and velocity, and how much time we had to deflect it, I think even something as large as that might be deflectable. Also if significant funding and attention was given to this problem, and people realized that the existence of life on Earth depended on it, I'm sure there'd be a lot of innovation, resulting in all sorts of other ideas and technologies that we haven't thought of yet. It's premature to throw up our hands and give up on preventing this incredibly dire threat without giving it a much more serious try than we've done so far.