We present fully self-consistent calculations of the thermodynamic properties of three-dimensional clean SNS Josephson junctions, where S is an s-wave short-coherence-length superconductor and N is a clean normal metal, The junction is modeled on an infinite cubic lattice such that the transverse width of the S is the same as that of the N, and its thickness is tuned from the short to long limit. Intrinsic effects, such as a reduced order parameter near the SN boundary and finite gap to Fermi energy ratio, depress the critical Josephson current I-c, even in short junctions. Our analysis is of relevance to experiments on SNS junctions which find much smaller I_cR_N products than expected from the standard (non-self-consistent and quasiclassical) predictions. We also find nonstandard current-phase relations, a counterintuitive spatial distribution of the self-consistently determined order parameter phase, and an unusual low-energy gap in the local density of states within the N region.