We investigate the performance of on-the-fly ab initio (OTF-AI) semiclassical dynamics combined with the thawed Gaussian approximation (TGA) for computing vibrationally resolved absorption and photoelectron spectra. Ammonia is used as a prototype of floppy molecules, whose potential energy surfaces display strong anharmonicity. We show that despite complications due to the presence of large amplitude motion, the main features of the spectra are captured by the OTF-AI-TGA, which -by definition- does not require any a priori knowledge of the potential energy surface. Moreover, the computed spectra are significantly better than those based on the popular global harmonic approximation. Finally, we probe the limit of the TGA to describe higher- resolution spectra, where long time dynamics is required.