We demonstrate, via simulations of asymptotically reduced equations describing rotationally constrained Rayleigh-Bénard convection, that the efficiency of turbulent motion in the fluid bulk limits overall heat transport and determines the scaling of the nondimensional Nusselt number Nu with the Rayleigh number Ra, the Ekman number E, and the Prandtl number σ. For E << 1 inviscid scaling theory predicts and simulations confirm the large Ra scaling law Nu-1 ≈ C(1)σ(-1/2)Ra(3/2)E(2), where C(1) is a constant, estimated as C(1) ≈ 0.04 ± 0.0025. In contrast, the corresponding result for nonrotating convection, Nu-1 ≈ C(2)Ra(α), is determined by the efficiency of the thermal boundary layers (laminar: 0.28 ≤ α ≤ 0.31, turbulent: α ~ 0.38). The 3/2 scaling law breaks down at Rayleigh numbers at which the thermal boundary layer loses rotational constraint, i.e., when the local Rossby number ≈ 1. The breakdown takes place while the bulk Rossby number is still small and results in a gradual transition to the nonrotating scaling law. For low Ekman numbers the location of this transition is independent of the mechanical boundary conditions.