Previous studies have examined separately how pollinator generalization and abundance influence plant reproductive success, but none so far has evaluated simultaneously the relative importance of these pollinator attributes. Here we evaluated the extent to which pollinator generalization and abundance influence plant reproductive success per visit and at the population level on a generalist plant, Opuntia sulphurea (Cactaceae). We used field experiments and path analysis to evaluate whether the per-visit effect is determined by the pollinator's degree of generalization, and whether the population level effect (pollinator impact) is determined by the pollinator's degree of generalization and abundance. Based on the models we tested, we concluded that the per-visit effect of a pollinator on plant reproduction was not determined by the pollinators' degree of generalization, while the population-level impact of a pollinator on plant reproduction was mainly determined by the pollinators' degree of generalization. Thus, generalist pollinators have the greatest species impact on pollination and reproductive success of O. sulphurea. According to our analysis this greatest impact of generalist pollinators may be partly explained by pollinator abundance. However, as abundance does not suffice as an explanation of pollinator impact, we suggest that vagility, need for resource consumption, and energetic efficiency of generalist pollinators may also contribute to determine a pollinator's impact on plant reproduction.