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We present new deep Very Large Telescope (VLT)/FORS optical spectra with intermediate resolution and large wavelength coverage of the compact radio source and ultra-luminous IR galaxy (ULIRG) PKS 1345+12 (4C 12.50; z= 0.122), taken with the aim of investigating the impact of the nuclear activity on the circumnuclear interstellar medium (ISM). PKS 1345+12 is a powerful quasar [L(Hβ)_NLR ∼ 10⁴² erg/s] and is also the best studied case of an emission line outflow in a ULIRG. Using the density-sensitive transauroral emission lines [S II]4068,4076 and [O II]7318,7319,7330,7331, we pilot a new technique to accurately model the electron density for cases in which it is not possible to use the traditional diagnostic [S II]6716/6731, namely sources with highly broadened complex emission line profiles and/or high (N_e ≳ 10⁴/cm3) electron densities. We measure electron densities of N_e= (2.94^+0.71_–1.03) {x} 10³/cm3, N_e= (1.47^+0.60_–0.47) {x} 10⁴/cm3 and N_e= (3.16^+1.66_–1.01) {x} 10⁵/cm3 for the regions emitting the narrow, broad and very broad components, respectively. We therefore calculate a total mass outflow rate of {dot}M = 8⁺²_–3 M_☉/yr, similar to the range estimated for another compact radio source, PKS 1549-79. We estimate the total mass in the warm gas outflow is M_total= (8⁺³_–3) x 10⁵ M_☉ with filling factors of ε= (4.4^+1.8_–1.5) x 10^–4 and ε= (1.6^+0.7_–0.5) {x} 10^–7 for the regions emitting the broad and very broad components, respectively. The total kinetic power in the warm outflow is {dot}E_total=(3.4^+1.5_–1.3)x10⁴² erg/s. Taking the black hole properties published by Dasyra et al., we find that only a small fraction [{dot}E/L_bol=(1.3±0.2 x 10^–3] of the available accretion power is driving the warm outflow in PKS 1345+12, which is significantly less than that currently required by the majority of quasar feedback models (∼5–10 per cent of L_bol), but similar to the recent suggestion of Hopkins & Elvis if a two-stage feedback model is implemented ( ∼ 0.5 per cent of L_bol). The models also predict that active galactic nuclei (AGN)-driven outflows will eventually remove the gas from the bulge of the host galaxy. Our observations show that the visible warm outflow in PKS 1345+12 is not currently capable of doing so. However, it is entirely possible that much of the outflow is either obscured by a dense and dusty natal cocoon and/or in cooler or hotter phases of the ISM. This result is important not just for studies of young Gigahertz-Peaked Spectrum/Compact Steep Spectrum radio sources, but for AGN in general.