We examine the signal from pump-probe spectroscopy of a model system-nonrotating I-2-at short time delays and compare signals calculated without approximation (a full quantum calculation), with a semiclassical Franck-Condon approximation, and with a classical simulation of the nuclear wave packet. In order to assess the complications of simulation and interpretation when the probe window lies in the spectroscopically and dynamically important Franck-Condon region, we concentrate on a case where pump and probe resonances are at the same internuclear distance. We find that the common practice of ignoring the pump-truncation effects of pulse overlap leads to an overestimate of the signal at short times. Moreover, both classical simulations and semiclassical Franck-Condon treatments can deviate significantly in form from the actual signal even with proper treatment of pulse overlap. The sources of these deviations can be seen in the evolution of the excited-state nuclear distributions calculated classically and under the semiclassical Franck-Condon approximation. Specifically, the differences in evolution of the classical and full quantum excited-state nuclear distributions are due to differing initial momentum distributions. We introduce an efficient method for calculating the pump-probe signal that takes advantage of the brevity of ultrashort pulses and can include pulse characteristics such as chirp. This short-pulse expansion method aids in the proper treatment of pulse-overlap and nonzero pulse duration and promises to simplify the incorporation of relaxation processes.