We establish that the behavior of fluids consisting of repulsive spheres under the combined effects of pressure p, temperature T, and applied shear stress s can be organized in a jamming phase diagram parameterized by the dimensionless quantities T/pd^3, s/p, and pd^3/e, where d is the diameter of the spheres and e is the interaction energy scale. The jamming phase diagram describes the three-dimensional parameter space as the product of an equilibrium plane at s/p=0 and a hard sphere plane at pd^3/e=0. Near the hard sphere plane, the jamming phase diagram is universal in the sense that material properties are insensitive to the details of the interaction potential. We demonstrate that within the universal regime, the conventional approach to the dynamic glass transition along a decreasing temperature trajectory is equivalent to the colloidal glass transition approach along an increasing pressure trajectory. Defining the dynamic glass transition by where a dimensionless relaxation time equals a large but arbitrary value, we measure a two-dimensional dynamic glass transition surface whose precise location depends on the choice of time scale but which always encloses the singular point at the origin, T/pd^3=s/p=pd^3/e=0. We show that at finite shear stress, the effective temperature Teff fluidizes the system in a similar way as the environment temperature T fluidizes the system in the absence of shear. We demonstrate that the dynamic glass transition surface is largely controlled a single parameter, the dimensionless effective temperature Teff/pd^3, that describes the competition between low frequency fluctuations and the confining pressure. Even well into the fluid portion of the jamming phase diagram, we show that relaxation is largely controlled by this single parameter, regardless of whether the fluctuations are created by temperature or shear. Finally, by investigating correlations in the dynamics as a function of length scale a and time scale t, we identify two types of pairs (a, t) over which the dynamics are maximally correlated, suggesting that kinetic heterogeneity is a general feature of dynamical crossovers and not necessarily an indication of an impending thermodynamic transition.