The Mission Accessible Near-Earth Object Survey (MANOS) aims to observe and characterize small (mean absolute magnitude H~25 mag) Near-Earth Objects (NEOs) that are accessible by spacecraft (mean {Delta}~5.7 km/s) and that make close approaches with the Earth (mean Minimum Orbital Intersection Distance MOID ~0.03 au). We present here the first results of the MANOS visible spectroscopic survey. The spectra were obtained from August 2013 to March 2018 at Lowell Observatory's Discovery Channel 4.3 m telescope, and both Gemini North and South facilities. In total, 210 NEOs have been observed and taxonomically classified. Our taxonomic distribution shows significant variations with respect to surveys of larger objects. We suspect these to be due to a dependence of Main Belt source regions on object size. Compared to previous surveys of larger objects, we report a lower fraction of S+Q-complex asteroids of 43.8+/-4.6%. We associate this decrease with a lack of Phocaea family members at very small size. We also report higher fractions of X-complex and A-type asteroids of 23.8+/-3.3% and 3.8+/-1.3% respectively due to an increase of Hungaria family objects at small size. We find a strong correlation between the Q/S ratio and perihelion distance. We suggest this correlation is due to planetary close encounters with Venus playing a major role in turning asteroids from S to Q-type. This hypothesis is supported by a similar correlation between the Q/S ratio and Venus MOID.