Maybe the Chinese will carry the torch
Since NASA isn't moving on nuclear propulsion, perhaps the Chinese will be the first ones to reach Mars. They've certainly got the ability to go in that direction if they want to. If the US is too timid to use nuclear power for in-space propulsion, someone else likely will.
Cooling a reactor in space would be an issue since only radiation cooling works there, but large radiator fins (shielded from the sun) could radiate the waste heat. They would probably have to be fairly large.
But nuclear is really the only way to go for in-space propulsion. Trying to explore space with chemical rockets is like trying to run a modern airline with gliders -- not going to work.