Nuclear thermal propulsion can potentially reduce the time of flight and spacecraft system mass needed for human spaceflight beyond cislunar space. This nuclear propulsion system has comparable thrust capability to chemically impulsive systems, which at about twice the specific impulse, can double the delta-velocity (ΔV) for the same propellant mass. However, the canonical problem for nuclear propulsion has always been that its benefits are shadowed by low technology readiness of a complex system. This paper describes a combined cycle nuclear thermal rocket (CCNTR) system architecture for propulsion and electrical power that comprises a 42-MWt-capable nuclear reactor core to provide 9.4 kN thrust on demand at a specific impulse of 940 s. The liquid hydrogen propellant flow through the rocket chamber cools the reactor during burns, thereby producing thrust while concurrently rejecting waste heat to space. The reactor also produces up to 100 kWe power for the spacecraft, eliminating the need for solar power generation and averting challenges associated with restarting a cold reactor for propulsive burns. Radiators reject the waste heat from electrical power production. Earth-to-Mars orbital transfers less than 100 days appear feasible assuming 680,000 kg of liquid hydrogen propellant and a vehicle dry mass of 83,000 kg that includes the 13,000 kg CCNTR system. Together, these results suggest that a CCNTR could be most promising to enable crewed missions to Mars.