Speech motor actions are performed quickly, while simultaneously maintaining a high degree of accuracy. Are speed and accuracy in conflict during speech production? Speed-accuracy tradeoffs have been shown in many domains of human motor action, but have not been directly examined in the domain of speech production. The present work seeks evidence for Fitts' law, a rigorous formulation of this fundamental tradeoff, in speech articulation kinematics by analyzing USC-TIMIT, a real-time magnetic resonance imaging data set of speech production. A theoretical framework for considering Fitts' law with respect to models of speech motor control is elucidated. Methodological challenges in seeking relationships consistent with Fitts' law are addressed, including the operational definitions and measurement of key variables in real-time MRI data. Results suggest the presence of speed-accuracy tradeoffs for certain types of speech production actions, with wide variability across syllable position, and substantial variability also across subjects. Coda consonant targets immediately following the syllabic nucleus show the strongest evidence of this tradeoff, with correlations as high as 0.72 between speed and accuracy. A discussion is provided concerning the potentially limited applicability of Fitts' law in the context of speech production, as well as the theoretical context for interpreting the results.