Getting to Mars in 2 months seems rather unrealistic- I doubt that the first nuclear spaceship could or will get to Mars this quickly. If this short travel time is supposed to be a sort of ultimate goal that may be realised decades from now, then maybe. BUT even if it's a longer term goal; it reminds of the Shuttle's goal of providing cheap access to space. Forgetting all the technical challenges, it seems to me that even if you had the capability if getting to Mars in two months, you would choose a slower travel time in order to get significantly more payload to Mars. If you compare getting to Mars in 4 months as compared to 2 months, there is no significant advantage- unless you want to have artifical gravity from the acceleration to Mars and the deceleration as you approach Mars [I don't know how much this would be but would guess it's somewhere around a constant 1/10th of a gee] AND you wanted so much mass (all the rocket propellant for the deceleration) that the radiation levels would be around what you have on the Earth surface. IF you had these sort of "requirements" then a 2 month travel time makes "sense".
If you were to compare a nuclear spacecraft which gets to Mars in 2 months to a chemical propulsion spacecraft which got to Mars in 4 months, and if you were to lift all the propellent from Earth, the chemical propulsion would require less mass lifted from Earth. Whereas if you were to compare a nuclear spacecraft with 4 month travel time to a chemical which had a 4 or even 6 month travel time then the nuclear would require less total mass lifted. Or let me say it a different way, making this Mars nuclear spacecraft get to Mars in 2 months would cost more money than anything offered by NASA so far. In other words this going to be too expensive, if the goal is 2 months to Mars.
Of course the obvious way of getting to Mars is by first exploring the Moon for minable water. This would be something which could be done in the short term and it's costs would be utterly insignificant as compared to Mars in 2 months (or NASA other plans of getting to Mars or Zubrin's plans).