In rubber friction studies it is often observed that the kinetic friction coefficient depends on the nominal contact pressure. This is usually due to frictional heating, which softens the rubber, increases the area of contact, and (in most cases) reduces the viscoelastic contribution to the friction. In this paper we present experimental results showing that the rubber friction also depends on the nominal contact pressure at such low sliding speed that frictional heating is negligible. This effect has important implications for rubber sliding dynamics, e.g., in the context of the tire-road grip. We attribute this effect to the viscoelastic coupling between the macroasperity contact regions, and present a simple earthquakelike model and numerical simulations supporting this picture. The mechanism for the dependency of the friction coefficient on the load considered is very general, and is relevant for non-rubber materials as well.