Previous research showed that threat-related faces, due to their intrinsic motivational relevance, capture attention more readily than neutral faces. Here we used a standard temporal order judgment (TOJ) task to assess whether negative (either angry or fearful) emotional faces, when competing with neutral faces for attention selection, may lead to a prior entry effect and hence be perceived as appearing first, especially when uncertainty is high regarding the order of the two onsets. We did not find evidence for this conjecture across five different experiments, despite the fact that participants were invariably influenced by asynchronies in the respective onsets of the two competing faces in the pair, and could reliably identify the emotion in the faces. Importantly, by systematically varying task demands across experiments, we could rule out confounds related to suboptimal stimulus presentation or inappropriate task demands. These findings challenge the notion of an early automatic capture of attention by (negative) emotion. Future studies are needed to investigate whether the lack of systematic bias of attention by emotion is imputed to the primacy of a non-emotional cue to resolve the TOJ task, which in turn prevents negative emotion to exert an early bottom-up influence on the guidance of spatial and temporal attention.