We present the results of an optical spectroscopic monitoring program targeting NGC 5548 as part of a larger multi-wavelength reverberation mapping campaign. The campaign spanned six months and achieved an almost daily cadence with observations from five ground-based telescopes. The H$\beta$ and He II $\lambda$4686 broad emission-line light curves lag that of the 5100 $\AA$ optical continuum by $4.17^{+0.36}_{-0.36}$ days and $0.79^{+0.35}_{-0.34}$ days, respectively. The H$\beta$ lag relative to the 1158 $\AA$ ultraviolet continuum light curve measured by the Hubble Space Telescope is roughly $\sim$50% longer than that measured against the optical continuum, and the lag difference is consistent with the observed lag between the optical and ultraviolet continua. This suggests that the characteristic radius of the broad-line region is $\sim$50% larger than the value inferred from optical data alone. We also measured velocity-resolved emission-line lags for H$\beta$ and found a complex velocity-lag structure with shorter lags in the line wings, indicative of a broad-line region dominated by Keplerian motion. The responses of both the H$\beta$ and He II $\lambda$4686 emission lines to the driving continuum changed significantly halfway through the campaign, a phenomenon also observed for C IV, Ly $\alpha$, He II(+O III]), and Si IV(+O IV]) during the same monitoring period. Finally, given the optical luminosity of NGC 5548 during our campaign, the measured H$\beta$ lag is a factor of five shorter than the expected value implied by the $R_\mathrm{BLR} - L_\mathrm{AGN}$ relation based on the past behavior of NGC 5548.