We employ a small x color glass condensate (CGC)+ nonrelativistic QCD (NRQCD) formalism to compute J/ψ production at low p(⊥) in proton-proton collisions at collider energies. Very good agreement is obtained for total cross sections, rapidity distributions, and low momentum p(⊥) distributions. Similar agreement is obtained for ψ' production. We observe an overlap region in p(⊥) where our results match smoothly to those obtained in a next-to-leading order collinearly factorized NRQCD formalism. The relative contribution of color singlet and color octet contributions can be quantified in the CGC+NRQCD framework, with the former contributing approximately 10% of the total cross section.