That is not the reason this thing that won't happen won't happen. Nuclear rockets have already been developed and tested all the way back in the 60s. It won't happen because amerikkka can't build anything and absolutely can't build all the things that this mission would require in two years.

The past few NASA Mars rovers were nuclear powered but launched by traditional rockets. In 2010, two years before Curiosity rover landed with a nuclear-powered system, the Spirit lander (landed 2004) had sent its final signal; it got stuck in a sand trap at an angle that prevented recharging via solar panel. The low Sun intensity, combined with dust and sand, make nuclear a compelling power source for Mars.

Now, this nuclear power source is not like a nuclear-powered submarine which has an active power plant based on fission of uranium-235. Instead, the spacecraft are powered by plutonium dioxide, which is yielded by reprocessing spent nuclear fuel. The plutonium dioxide naturally decays, giving off a consistent ~100 watts of heat, which is then used to charge lithium batteries which, in turn, power the craft.^1

Nuclear power was also used in the pair of Voyager spacecraft sent in the late 70s and early 80s and are still communicating today. Because the decay rate of plutonium oxide declines over time (half life of about 87 years), the Voyagers have had to progressively shut down scientific instruments in order to preserve communication back to earth. IIRC, they are basically only sending pings “heartbeats” now.