Project Orion was a US-study of a spacecraft intended to be directly propelled by a series of explosions of atomic bombs behind the craft. The performance of nuclear spaceships means taking 50 passengers to Mars and back with no problems. In one second the craft produces more thrust than the puny chemical energy Saturn 5 Moon Rockets entire filled "soda can" has on launch.
This project was stopped because of cold war for reasons now obsolete. The technology needs to be built, for it is the only sensible and potent (i.e. not a firecracker) way to move in space. In an Armageddon type scenario, we either have the right tools or we perish. An Orion type spaceship in itself can be used to shove asteroids of-course just by turning the ship around to make the asteroid into an Orion space ship.