Clathrin-mediated endocytosis (CME), the major cellular entry pathway, starts when clathrin assembles on the plasma membrane into clathrin-coated pits (CCPs). Two populations of CCPs are detected within the same cell: 'productive' CCPs that invaginate and pinch off, forming clathrin-coated vesicles (CCVs) [1, 2], and 'abortive' CCPs [3, 4, 5] that prematurely disassemble. The mechanisms of gating between these two populations and their relations to the functions of dozens of early-acting endocytic accessory proteins (EAPs) [5, 6, 7, 8, 9] have remained elusive. Here, we use experimentally-guided modeling to integrate the clathrin machinery and membrane mechanics in a single dynamical system. We show that the split between the two populations is an emergent property of this system, in which a switch between an Open state and a Closed state follows from the competition between the chemical energy of the clathrin basket and the mechanical energy of membrane bending. In silico experiments revealed an abrupt transition between the two states that acutely depends on the strength of the clathrin basket. This critical strength is lowered by membrane-bending EAPs [10, 11, 12]. Thus, CME is poised to be shifted between abortive and productive events by small changes in membrane curvature and/or coat stability. This model clarifies the workings of a putative endocytic checkpoint whose existence was previously proposed based on statistical analyses of the lifetime distributions of CCPs [4, 13]. Overall, a mechanistic framework is established to elucidate the diverse and redundant functions of EAPs in regulating CME progression.