The NTR is a proven technology that generates high thrust and has a specific impulse (I sp ~900 s) twice that of today's best chemical rockets. During the Rover and NERVA (Nuclear Engine for Rocket Vehicle Applications) programs, twenty rocket reactors were designed, built and ground tested. These tests demonstrated: (1) a wide range of thrust; (2) high temperature carbide-based nuclear fuel; (3) sustained engine operation; (4) accumulated lifetime; and (5) restart capability-all the requirements needed for a human mission to Mars. Ceramic metal fuel was also evaluated as a backup option. In NASA's recent Mars Design reference Architecture (DRA) 5.0 study, the NTR was selected as the preferred propulsion option because of its proven technology, higher performance, lower launch mass, versatile vehicle design, simple assembly, and growth potential. In contrast to other advanced propulsion options, NTP requires no large technology scale-ups. In fact, the smallest engine tested during the Rover program-the 25 klb f "Pewee" engine is sufficient for a human Mars mission when used in a clustered engine configuration. The "Copernicus" crewed NTR Mars transfer vehicle design developed for DRA 5.0 has significant capability that can enable reusable "1-year" round trip human missions to candidate near Earth asteroids (NEAs) like 1991 JW in 2027, or 2000 SG344 and Apophis in 2028. A robotic precursor mission to 2000 SG344 in late 2023 could provide an attractive Flight Technology Demonstration of a small NTR engine that is scalable to the 25 klb f-class engine used for human missions 5 years later. In addition to the detailed scientific data gathered from on-site inspection, human NEA missions would also provide a valuable "check out" function for key elements of the NTR transfer vehicle (its propulsion module, TransHab and life support systems, etc.) in a "deep space" environment prior to undertaking the longer duration Mars orbital and landing missions that would follow. The initial mass in low Earth orbit required for a mission to Apophis is ~323 t consisting of the NTR propulsion module (~138 t), the integrated saddle truss and LH 2 drop tank assembly (~123 t), and the 6-crew payload element (~62 t). The later includes a multi-mission Space Excursion Vehicle (MMSEV) used for close-up examination and sample gathering. The total burn time and required restarts on the three 25 klb f "Pewee-class" engines operating at I sp ~906 s, are ~76.2 minutes and 4, respectively, well below the 2 hours and 27 restarts demonstrated on the NERVA eXperimental Engine, the NRX-XE. The paper examines the benefits, requirements and characteristics of using NTP for the above NEA missions. The impacts on vehicle design of HLV payload volume and lift capability, crew size, and reusability are also quantified.