The US did build a nuclear powered ramjet engine and test it. This isn't an insurmountable hurdle, it's an achieved one. The design they used of course has lots of good reasons we should not use it on Earth (namely, the reactor would activate the air, meaning it spews a plume of oxygen and nitrogen isotopes) but it does work.
You can solve the radionucleotide problem by running it off hydrogen instead, which doesn't activate in any meaningful quantity.
Basically, not only do we have the ability, we had it in 1961.
Interesting. That requires an atmosphere though; it might work for the first stage of a launch from Earth, and maybe even for Mars. Once you're out of the atmosphere you'd need some other method of propulsion.
I think nuclear space propulsion would be used as a reactor generating energy for ionic drive. That would work as a Mars-Earth shuttle while never going into atmosphere. The landing to and launching from the plane surface would be done by regular chemical rockets.
Specifically it requires propellant, which on Earth is the air intake. For space travel you have to still take a propellant, but it can be essentially any type of gaseous reaction mass - for example, water.
The US did build a nuclear powered ramjet engine and test it. This isn't an insurmountable hurdle, it's an achieved one. The design they used of course has lots of good reasons we should not use it on Earth (namely, the reactor would activate the air, meaning it spews a plume of oxygen and nitrogen isotopes) but it does work.
You can solve the radionucleotide problem by running it off hydrogen instead, which doesn't activate in any meaningful quantity.
Basically, not only do we have the ability, we had it in 1961.