The electronic structure and size scaling of spectroscopic observables in conjugated polymers are investigated using time-dependent density functional theory. We show that local density approximations and gradient-corrected functionals do not have an effective attractive Coulomb interaction between photoexcited electron-hole pairs to form bound states and therefore do not reproduce finite exciton sizes. Long-range nonlocal and nonadiabatic density functional corrections (such as hybrid mixing with an exact Hartree-Fock exchange) are necessary to capture correct delocalization of photoexcitations in one-dimensional polymeric chains.