Rockets do not "push against" anything. The whole business is momentum transfer.
Yes, I understand that, but this is not a traditional rocket. I found the answer on another website:
"The propulsion system advocated for the Orion spacecraft was based on an idea first put forward by Stanislaw Ulam and Cornelius Everett in a classified paper in 1955. Ulam and Everett suggested releasing atomic bombs behind a spacecraft, followed by disks made of solid propellant. The bombs would explode, vaporizing the material of the disks and converting it into hot plasma. As this plasma rushed out in all directions, some of it would catch up with the spacecraft, impinge upon a pusher plate, and so drive the vehicle forward.
Ulam and Everett's idea was modified so that instead of propellant disks, the propellant and bomb were combined into a single pulse unit. Plastic was chosen as the propellant material, not only because of its effectiveness in absorbing the neutrons emitted by an atomic explosion but also because it breaks down into lightweight atoms such as those of hydrogen and carbon which move at high speed when hot. This approach, in tandem with the pusher plate concept, offered a unique propulsion system that could simultaneously produce high thrust with high exhaust velocity. "
So, the vaporized plastic is what I was looking for. More than just a bomb is necessary.