  We present a search for extremely red, dust-obscured, $z>7$ galaxies with
$\textit{JWST}$/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 ($\sim 2.5$ mag) and detection in
MIRI/F770W ($\sim 25$ mag), we identify two galaxies$\unicode{x2014}$COS-z8M1
and CEERS-z7M1$\unicode{x2014}$which have best-fit photometric redshifts of
$z=8.5^{+0.3}_{-0.4}$ and $z=7.6^{+0.1}_{-0.1}$, respectively. We perform SED
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 ($R_{\rm eff} \lesssim 200$ pc), highly obscured ($A_V \sim
1.5$$\unicode{x2013}$$2.5$), and, at our best-fit redshift estimates, likely
have strong [OIII]+H$\beta$ emission contributing to their $4.4\,\mu$m
photometry. We estimate stellar masses of $\sim 10^{10}~M_\odot$ 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 AGN. We
identify a marginal (2.9$\sigma$) ALMA detection at 2 mm within $0.5''$ of
COS-z8M1, which if real, would suggest a remarkably high IR luminosity of $\sim
10^{12} L_\odot$. These two galaxies, if confirmed at $z\sim 8$, would be
extreme in their stellar and dust masses, and may be representative of a
substantial population of modestly dust-obscured galaxies at cosmic dawn.
