The anticorrelation between quantum efficiency (QE) and electron spin polarization (ESP) from a p-doped GaAs activated to negative electron affinity (NEA) is studied in detail using an ensemble Monte Carlo approach. The photoabsorption, momentum and spin relaxation during transport, and tunnelling of electrons through the surface potential barrier are modeled to identify fundamental mechanisms, which limit the efficiency of GaAs spin-polarized electron sources. In particular, we study the response of QE and ESP to various parameters such as the photoexcitation energy, doping density, and electron affinity level. Our modeling results for various transport and emission characteristics are in a good agreement with available experimental data. Our findings show that the behaviour of both QE and ESP at room temperature can be fully explained by the bulk relaxation mechanisms and the time which electrons spend in the material before being emitted.