Bringing from Earth a few tons of nuclear-powered jet engine to use water as propellant would take building such an engine first. We're not even close.
Chemical engines are lightweight and well-understood. Lifting kilotons of chemical fuel is not feasible, though. So we need to build an orbital chemical / cryo facility to produce at least something as simple as liquid hydrogen and liquid oxygen, again by the kiloton.
This is on top of building an orbital shipyard to construct the actual spaceship, with all that heavy shielding around it, and the skeleton to carry it, the fuel, and the habitable compartment. It's going to be a spectacular feat of space-borne metallurgy, mechanical processing, including precise machining, quite some chemistry to support that all and produce necessary plastic parts, saying nothing about the power plant to feed this all.
Here we assume that we have an asteroid that has enough metals, carbon, and water neatly parked on Earth orbit. How do we achieve that, and how many decades would it take to bring it here, is not even considered.
This all would be great to have! But getting straight to Mars seems simple in comparison.