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We present an investigation into the impact of feedback from outflowing UV and X-ray absorbers in nearby (z < 0.04) active galactic nuclei (AGNs). From studies of the kinematics, physical conditions, and variability of the absorbers in the literature, we calculate the possible ranges in the total mass outflow rate ({dot}M_out) and kinetic luminosity (L_KE) for each AGN, summed over all of its absorbers. These calculations make use of values (or limits) for the radial locations of the absorbers determined from variability, excited-state absorption, and other considerations. From a sample of 10 Seyfert 1 galaxies with detailed photoionization models for their absorbers, we find that 7 have sufficient constraints on the absorber locations to determine {dot}M_out and L_KE. For the low-luminosity AGN NGC 4395, these values are low, although we do not have sufficient constraints on the X-ray absorbers to make definitive conclusions. At least five of the six Seyfert 1s with moderate bolometric luminosities (L_bol= 10⁴³ - 10⁴⁵ erg/s) have mass outflow rates that are 10-1000 times the mass accretion rates needed to generate their observed luminosities, indicating that most of the mass outflow originates from outside the inner accretion disk. Three of these (NGC 4051, NGC 3516, and NGC 3783) have L_KE in the range 0.5%-5% L_bol, which is the range typically required by feedback models for efficient self-regulation of black hole and galactic bulge growth. At least two of the other three (NGC 5548, NGC 4151, and NGC 7469) have L_KE ≳ 0.1%L_bol, although these values may increase if radial locations can be determined for more of the absorbers. We conclude that the outflowing UV and X-ray absorbers in moderate-luminosity AGNs have the potential to deliver significant feedback to their environments.