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-1] 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 (Ne ≳ 104 cm-3) electron densities.We measure electron densities of Ne = (2.94+0.71-1.03)× 103 cm-3, Ne = (1.47+0.60-0.47) × 104 cm-3 and Ne = (3.16+1.66-1.01) × 105 cm-3 for the regions emitting the narrow, broad and very broad components, respectively. We therefore calculate a total mass outflow rate of M = 8+2-3M⊙ yr-1, similar to the range estimated for another compact radio source, PKS 1549-79. We estimate the total mass in the warm gas outflow is Mtotal = (8+3-3)×105M⊙ with filling factors of ∈ = (4.4+1.8-1.5)×10-4 and ∈ = (1.6+0.7-0.5)×10-7 for the regions emitting the broad and very broad components, respectively. The total kinetic power in the warm outflow is Ėtotal = (3.4+1.5-1.3)×1042 erg s-1. Taking the black hole properties published by Dasyra et al., we find that only a small fraction [Ė/Lbol = (1.3 ± 0.2) × 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 Lbol), but similar to the recent suggestion of Hopkins & Elvis if a two-stage feedback model is implemented (~0.5 per cent of Lbol). 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.