We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two-dimensional spherocylinders and three-dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter α → 0 and particles approach spherical. We find that the nematic order parameter S2 is nonmonotonic in the packing fraction ϕ and that, as α → 0, S2 stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming and that particle contacts preferentially lie along the narrowest width of the particles, even as α → 0.