It sounds like science fiction - maybe from Peter Hamilton in one of his nihilistic moments.
Yet, this project was called SLAM or Pluto, and in fact it reached a quite advanced development stage in the USA during the late 50's and early 60's. This awesome weapon system was intended to be faster than bombers, and especially to have far longer range - in fact, the nuclear reactor gave it nearly unlimited autonomy.
Developing this weapon was particularly challenging, because it required unprecedented performance from all its components, which had to operate in extreme environments due to temperature, radiation flux and mechanical stresses. Many of these components had to be invented from scratch, such as the ceramic fuel elements of the propulsion reactor.
A huge test facility in the Nevada desert was built in order to test the nuclear engines; two of them were in fact built and tested succesfully, the second one at full power. Also the revolutionary terrain contour navigation system was developed specifically for this application; nowadays it is at the core of all cruise missile guidance systems.
The project was eventually terminated in 1964, because ICBMs were faster, less expensive and way harder to intercept. Moreover, the SLAM had massive serious issues, being as much dangerous for friends and foes alike.
Yet, many of the scientists and engineers working on the SLAM remember fondly those years: it was a stimulating and challenging work environment, at the cutting edge of known technology. Ultimately, we have been spared one of the nastiest weapons ever devised, but that project yielded useful technological advencements.