We present a search for extremely red, dust-obscured, z > 7 galaxies with JWST/NIRCam+MIRI imaging over the first 20 arcmin(2) of publicly available Cycle 1 data from the COSMOS-Web, CEERS, and PRIMER surveys. Based on their red color in F277W-F444W (similar to 2.5 mag) and detection in MIRI/F770W (similar to 25 mag), we identify two galaxies, COS-z8M1 and CEERS-z7M1, that have best-fit photometric redshifts of z = 8.4(-0.4)(+0.3) and 7.6(-0.1)(+0.1), respectively. We perform spectral energy distribution fitting with a variety of codes (including BAGPIPES, PROSPECTOR, BEAGLE, and CIGALE) and find a >95% probability that these indeed lie at z > 7. Both sources are compact (R-eff less than or similar to 200 pc) and highly obscured (A(V) similar to 1.5-2.5) and, at our best-fit redshift estimates, likely have strong [O III]+H beta emission contributing to their 4.4 mu m photometry. We estimate stellar masses of similar to 10(10) M-circle dot for both sources; by virtue of detection in MIRI at 7.7 mu m, these measurements are robust to the inclusion of bright emission lines, for example, from an active galactic nucleus. We identify a marginal (2.9 sigma) Atacama Large Millimeter/submillimeter Array detection at 2 mm within 0 ''.5 of COS-z8M1, which, if real, would suggest a remarkably high IR luminosity of similar to 10(12) L-circle dot. These two galaxies, if confirmed at z similar to 8, would be extreme in their stellar and dust masses and may be representative of a substantial population of highly dust-obscured galaxies at cosmic dawn.