We present observations from the Transiting Exoplanet Survey Satellite (TESS) of twenty bright core-collapse supernovae with peak TESS-band magnitudes <18 mag. We reduce this data with an implementation of the image subtraction pipeline used by ASAS-SN optimized for use with the TESS images. In empirical fits to the rising light curves, we do not find strong correlations between the fit parameters and the peak luminosity. Existing semi-analytic models fit the light curves of the Type II SNe well, but do not yield reasonable estimates of the progenitor radius or explosion energy, likely because they are derived for use with ultraviolet observations while TESS observes in the near-infrared. If we instead fit the data with numerically simulated light curves, the rising light curves are consistent with the explosions of red supergiants. While we do not identify shock breakout emission for any individual event, when we combine the fit residuals of the Type II supernovae in our sample we do find a >5 sigma flux excess in the ~0.5 days before the start of the light curve rise. It is likely that this excess is due to shock breakout emission, and that during its extended mission TESS will observe a Type II supernova bright enough for this signal to be detected directly.