The breakup of droplets in an inhomogeneous flow is the key to emulsification. Frequently, the local flow experienced by the drops is a (quasi-) simple shear flow. The breakup of droplets in a steady, simple shear flow in the absence of emulsifiers has been studied extensively. In the presence of emulsifiers, the droplet interface may acquire viscoelastic properties, which are important in the prevention of coalescence, but their influence on droplet breakup has not been established solidly. This article reports on a phenomenological approach, which links the droplet breakup dynamics to the interfacial viscoelasticity, identifying the latter with the elasticity modulus of a deforming planar interface. Over a viscosity ratio range of three decades, the results have been found to agree with the model, which uses only independently known quantifies derived from equilibrium interfacial tension properties.