Organic oligomers and polymers with extended pi-conjugation are the fundamental building blocks of organic electronic devices. Novel routes are being explored to create tailor-made organic materials, and recent progress in organic chemistry and surface chemistry has led to the synthesis of planar 2D polymers. Here we show how extending pi-conjugation in the second dimension leads to novel materials with HOMO-LUMO gaps smaller than in ID polymers built from the same parent molecular repeat unit. Density functional theory calculations on experimentally realized 2D polymers grant insight into HOMO-LUMO gap contraction with increasing oligomer size and show fundamental differences between ID and 2D "band gap engineering". We discuss how the effects of cross-conjugation and dihedral twists affect the electronic gaps.