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The Off-plane Grating Rocket Experiment (OGRE) is a soft X-ray grating spectrometer to be flown on a suborbital rocket. The payload is designed to obtain the highest-resolution soft X-ray spectrum of Capella to date with a resolution goal of $R(\lambda/\Delta\lambda)>2000$ at select wavelengths in its 10--55 Angstrom bandpass of interest. The optical design of the spectrometer realizes a theoretical maximum resolution of $R\approx5000$, but this performance does not consider the finite performance of the individual spectrometer components, misalignments between components, and in-flight pointing errors. These errors all degrade the performance of the spectrometer from its theoretical maximum. A comprehensive line-spread function (LSF) error budget has been constructed for the OGRE spectrometer to identify contributions to the LSF, to determine how each of these affects the LSF, and to inform performance requirements and alignment tolerances for the spectrometer. In this document, the comprehensive LSF error budget for the OGRE spectrometer is presented, the resulting errors are validated via raytrace simulations, and the implications of these results are discussed., Comment: 26 pages, 9 figures, preprint of a manuscript accepted for publication in the Journal of Astronomical Telescopes, Instruments, and Systems (JATIS)