When speaking in any language, speakers must conceptualize what they want to say before they can formulate and articulate their message. We present two experiments employing a novel experimental paradigm in which the formulating and articulating stages of speech production were kept identical across conditions of differing conceptualizing difficulty. We tracked the effect of difficulty in conceptualizing during the generation of speech (Experiment 1) and during the abandonment and regeneration of speech (Experiment 2) on speaking fluency by Dutch native speakers in their first (L1) and second (L2) language (English). The results showed that abandoning and especially regenerating a speech plan taxes the speaker, leading to disfluencies. For most fluency measures, the increases in disfluency were similar across L1 and L2. However, a significant interaction revealed that abandoning and regenerating a speech plan increases the time needed to solve conceptual difficulties while speaking in the L2 to a greater degree than in the L1. This finding supports theories in which cognitive resources for conceptualizing are shared with those used for later stages of speech planning. Furthermore, a practical implication for language assessment is that increasing the conceptual difficulty of speaking tasks should be considered with caution.