The scaling of reaction yields in light ion fusion to low reaction energies is important for our understanding of stellar fuel chains and the development of future energy technologies. Experiments become progressively more challenging at lower reaction energies due to the exponential drop of fusion cross sections below the Coulomb barrier. We report on experiments where deuterium-deuterium (D-D) fusion reactions are studied in a pulsed plasma in the glow discharge regime using a benchtop apparatus. We model plasma conditions using particle-in-cell codes. Advantages of this approach are relatively high peak ion currents and current densities (0.1 to several A/cm2) that can be applied to metal wire cathodes for several days. We detect neutrons from D-D reactions with scintillator-based detectors. For palladium targets, we find neutron yields as a function of cathode voltage that are over 100 times higher than yields expected for bare nuclei fusion at ion energies below 2 keV (center of mass frame). A possible explanation is a correction to the ion energy due to an electron screening potential of 1000 ± 250 eV, which increases the probability for tunneling through the repulsive Coulomb barrier. Our compact, robust setup enables parametric studies of this effect at relatively low reaction energies.