Small nukes? See Project Orion - nuclear pulse engines. “Mars by 1965, Saturn by 1970”
Smallest ship would have carried a crew of 150 ... Fresh water by the tons used on outer shell as insulation from particles. Interstellar versions planned. Killed 1965
“Sixteen stories high, shaped like the tip of a bullet, and with a pusher plate 41m in diameter, the spacecraft would have utilized a launch pad composed of eight towers, each 76m high. Remarkably, most of the takeoff mass of about 10,000 tons would have gone into orbit. The bomb units ejected on takeoff at a rate of one per second would have yielded 0.1 kiloton; then, as the vehicle accelerated, the ejection rate would have slowed and the yield increased, until 20-kiloton bombs would have been exploding every 10 seconds.”
The whole of this rested on designing very small, efficient, reliable nukes - the only guy who could do it well left the field ... has someone else picked it up? Don’t know, but these are also tactial battlefield nuclear weapons. The other problem was steering the ship precisely.
To Mars By A Bomb - The Secret History of Project Orion (Nuclear Propulsion)
https://www.youtube.com/watch?v=xYoLcJuBtOw
I guess that Orion was just ahead of its time.
The risks of fast tracking that system back in the 1960’s would have been quite high. The bugs had not yet been worked out for living in space. The design was a hugely inefficient brute force approach - the great bulk of the energy was dissipated, with only a tiny fraction providing thrust. And it was pretty dirty - a thousand plutonium bombs to liftoff, with no solution for the fallout. Also, if there was a single Challenger-like malfunction (which were more common back then), it would burn in with thousands of warheads aboard - goodbye to the careers of all decision makers involved. Also, if we developed it, it would be subject to proliferation through espionage - just like our nuclear weapons programs were.
I would guess that after two terms of Clinton, and two terms of Obama, that the Chinese have the full files on this project, as well as the rest of our programs (e.g. Wen Ho Lee), so maybe they will build one for military use.
It is still probably a leading solution for the planetary defense mission of diverting an asteroid impact. if that would ever be funded. I imagine that by now there would be significant refinement of a lot of components, so that a freshly designed system could use and adjust the thrust much more efficiently. George Dyson alluded to that in the video you linked.
An updated Orion-like propulsion system might even be used for heavy lift operations around the solar system, like the mining envisioned in the article of this thread.
There is no doubt in my mind though, that we you want to accomplish big things in space, we need to use nuclear power.