Looking at the situation objectively, we will either destroy ourselves, or incidentally gain rocket technology capable of destroying an asteroid long before an extinction-level event occurs. There is no reason to make asteroid deflection a priority. There are far more pressing threats to the human race. Mostly the human race itself - and the humanities are the best defense against humans.
You realize that Armageddon was just a Hollywood movie, right? :-) I am not sure if the same thing would be feasible in the real world, with current technology.
Nor am I convinced that we will eventually be able to escape our dieing sun, but I keep my fingers crossed.
Unless we have a good couple years of advanced notice so we can gently push it in another direction, nukes are the best option. If you spread the thing wide enough, less of it will hit you. If the pieces are small enough, chances are few of them will do any damage.
It won't do much good if the thing is the size of a state, but mountain-sized rocks seem manageable this way.
