A series of experiments [C. Poulard and A. M. Cazabat, "Spontaneous spreading of nematic liquid crystals," Langmuir21, 6270 (2005)] on spreading droplets of nematic liquid crystal (NLC) reveals a surprisingly rich variety of behaviors. Small droplets can either be arrested in their spreading, spread stably, destabilize without spreading (corrugated surface), or spread with a fingering instability and corrugated free surface. In this work, we discuss the problem of NLC drops spreading in a simplified two-dimensional (2D) geometry. The model that we present is based on a long-wavelength approach for NLCs by Ben Amar and Cummings ["Fingering instabilities in driven thin nematic films," Phys. Fluids13, 1160 (2001); L. J. Cummings, "Evolution of a thin film of nematic liquid crystal with anisotropic surface energy," Eur. J. Appl. Math.15, 651 (2004)]. The improvements in the model here permit fully nonlinear time-dependent simulations. These simulations, for the appropriate choice of parameter values, exhibit 2D versions of most of the phenomena mentioned above.