Problems with the nuke idea
What if the space rock is too big for one or even a few nuclear bombs?
Armaggedon made the public think that one nuke buried 800 feet below
the surface of a planetoid the size of Texas could do the trick.
What if the nuke does split up the object, but that just turns it into
more pieces still aiming for Earth at high speed?
I think the idea of putting rocket motors on the rock to push it just far
enough off its course might work. If we have time, that is. Otherwise
I recognize that the nuke option might be our only one, but see above.
As Carl Sagan once said, NEOs are nature's way of telling intelligence
species to start colonizing space or else. The dinosaurs didn't listen in
time and look what happened.