We utilize a custom-built shear cell mounted on a confocal microscope to directly visualize and quantify the microdynamic mechanisms that mediate the rheology of a nearly jammed colloidal suspension under constant-stress deformation, with and without attractive interparticle interactions. The application of external stresses systematically increases particle mobility, as well as the ease by which the colloids can escape from topological cages formed by their nearest neighbors. We quantify the characteristic size and timescale of microstructural rearrangements within the suspension and show that these relaxation events become less spatiotemporally heterogeneous as the applied stress is increased. When interparticle attraction is introduced, the colloids tend to move more congruently under low stresses and the characteristic size of dynamically cooperative clusters increases. However, particle displacements become decorrelated under large external loads, with an abrupt transition occurring at the yield stress. In contrast, the repulsive system shows a more gradual transition from creep deformation to flow, with a nonmonotonic dependence of the particle displacement correlation function on the applied stress. Our results contribute to a better understanding of the jamming phase diagram in disordered colloidal materials, and the connection between the microstructure and nonlinear rheology of colloidal gels and glasses. (C) 2014 The Society of Rheology.