Though I'm not against the idea of nuclear powered spacecraft, I don't see the necessity for it to get to Mars.
I think nuclear reactors on Mars may be something more compelling. I think nuclear reactors on the Moon would be good idea- on Mars it's an even better idea.

One problem in regards to nuclear propulsion is it might be better suited [or required] for longer distances than Mars. If one were to accelerate for say a week's time one is forced towards more exotic solutions than chemical rockets. The Shuttle burns it's engines to get into orbit for about 7 mins. It's not "economical" for a nuclear rocket [unless it's something like the Orion] to use a nuclear engine for short burns [something less than say 10 minutes].
One way to look at this is with a chemical rocket one's engine mass is relative small compared rocket fuel mass. With A nuclear engine one tends to have more massive engines as compared to fuel- it doesn't cost much in terms mass to have a powerful chemical engine, unlike a nuclear engine.

Another way to look at it is if you want to get to Mars in 2 months time [and not use a cycler] than one is almost forced to nuclear power type option [and probably accelerate for most of that 2 month period {accelerating then decelerating}, but if 4-5 months is an acceptable duration for the trip, then you can use chemical rockets.

If one's goal is to get to Mars in 4-5 months and return to Earth in 4-5 months, much of the radiation problem will be solved- first because one is reducing the trip time, and second you would be required to decelerate as you approach Mars [therefore that fuel needed can function as shielding].

NASA spends more than $10,000 per lb of payload using the Shuttle to get to orbit. As sure as gravity, whatever NASA makes to go to the Moon will cost $20,000 per lb of payload- though probably closer to $30,000 per lb, and any manned spacecraft going to Mars will at minimal be $30,000 per lb.
Now, the private sector routinely delivers payload at 1/2 or less than the cost that NASA does.

If NASA didn't have to worry about radiation [used 9 month trajectory], most of the payload mass to get to Mars trajectory would be rocket fuel. If a seven month trajectory one needs even more of the mass being rocket fuel.

So, instead of NASA lifting the rocket fuel at more $20,000 per lb, what if it could buy the fuel needed at half the cost already delivered by the private sector? NASA could afford to use more fuel- roughly twice as fuel at the same cost.

So this would "work" if the private sector merely shipped the rocket fuel, but the private sector could also make the fuel in Space and sell it at same cost of shipping from Earth or less. One factor to whether the private would mine water in space and convert to rocket fuel, would depend upon the comparative cost of shipping a certain quantity as compared to total cost mining and making rocket fuel.

Generally speaking, the more quantity needed the more likely mining water and making rocket fuel could be a lower cost than shipping from Earth.
A million lbs of rocket fuel selling for $5000 per lb at L-1, is 5 billion dollars of gross product. 5 billion dollars would probably be less than the cost of entire operation needed to mine water and convert into fuel- so with only NASA as the customer with total revenue being 5 billion dollars it wouldn't be profitable. But anyone in the private sector with a NASA contract to buy million tonnes of rocket at $5000 per lb could make it profitable by getting other market share from other parties. In other words, NASA contract could serve as an anchor tenant.

Of NASA in it's brilliance and general govt corruption, could opt to paid twice as much: 10 billion for million lbs, but still even at this price it's still getting a bargain. Btw, if NASA paid the higher price companies would probably prefer to ship from Earth- simpler and less risk. But it's likely that eventually someone would invest in lunar mining- a market would be already be established, cost shipping to L-1 would get lower and someone would take the risks to get a profit with expectation of higher volume demand in the future- assuming there was minable water on the Moon.

So, whatever NASA using to get to the Moon, with some modification could than be used to get to Mars- it gets to L-1 with emptying tank getting there, refills the tanks and then could get to Mars- but not fast enough. So you get another "stage" to give it an additional boost, say 3-4 km/sec, this stage accelerates the Mars craft towards Earth, and at Earth perigee, the Mars craft fires it boosters. The first stage can decelerate and go back to L-1, or perhaps continue to go to Mars at different trajectory and time than Mars spacecraft.

You would need a gas station at Mars orbit and another first stage booster. Buying fuel at Mars orbit may cost twice as much, though 50% more would be a non- NASA as usual sort of price. You of course could ship the fuel to Mars at lower delta-v slower trajectories. Eventually, if water and power was cheaper on Mars, then one might be able to ship rocket fuel from Mars surface to it's orbit at a lower cost.

Apollo Command Service Module gross weight was 66,863 lb with Propellants weight of 40,759 lb with "Spacecraft delta v: 2,804 m/s"
http://www.astronautix.com/craft/apolocsm.htm

So very roughly, manned Mars craft might use 50,000 lbs of fuel, and first stage booster could be around 150,000 of fuel.
So million lb of rocket could give around 5 one way trips- probably more like 4.