>What about a really heavy massed asteroid.

Elementary physics: a heavy asteroid will be attracted just as much as a light one.

>A nuclear launch system is much less complex than a modern space launch system

A nuclear launch system is first and foremost less capable than a modern space launcher. Try leaving LEO with a stock ICBM.

Nukes are a very poor way to deflect asteroids. It's not so much about the bomb's complexity, but the result of the explosion is hard to predict. You don't know enough about the asteroids composition.
Even if you can get a significant impulse out of the explosion in the first place (and that requires getting close, probably even landing - see Hayabusa/Minerva if you think that's so easy), as long as you don't hit the center of gravity you just might send it spinning.