Keeping Mount Everest -- (dinosaur ending size asteroids) away from Earth

Keeping Mount Everest -- (dinosaur ending size asteroid) away from Earth:

Nuclear powered rocket engines – when we get around to developing them – are envisioned super heating indigenous gases (e.g., Martian atmosphere) to create thrust. Such an engine attached to an asteroid could conceivably be capable of vaporizing some of the rock to create thrust.  Then it's just a matter of attaching a guidance system and to vector the thrust. Problem solved.

We could have been working on nuclear powered rocket engines for the past 25 years while we've been wasting $1 billion a shot on our ancient technology space shuttle -- or on the $100 billion space station which as far as I can see only researches how much time astronauts can stay together without getting into fights.