  We study a new population of extremely red objects (EROs) recently discovered
by JWST based on their NIRCam colors F277W$-$F444W $>1.5$ mag. We find 37 EROs
in the CEERS field with F444W $<28$ mag and photometric redshifts between
$5<z<7$, with median $z=6.9^{+1.0}_{-1.6}$. Surprisingly, despite their red
long-wavelength colors, these EROs have blue short-wavelength colors
(F150W$-$F200W$\sim$0 mag) indicative of bimodal SEDs with a red, steep slope
in the rest-frame optical, and a blue, flat slope in the rest-frame UV.
Moreover, all these EROs are unresolved, point-like sources in all NIRCam
bands. We analyze the spectral energy distributions of 8 of them with MIRI and
NIRSpec observations using stellar population models and AGN templates. We find
that a dusty galaxy or an obscured AGN provide similarly good SED fits but
different stellar properties: massive and dusty, log M/M_sun$\sim$10 and
A$_{\rm V}\gtrsim3$ mag, or low mass and obscuration, log M/M_sun$\sim$7.5 and
A$_{\rm V}\sim0$ mag, hosting an obscured QSO. SED modeling does not favor
either scenario, but their unresolved sizes are more suggestive of an AGN. If
any EROs are confirmed to have log M/M_sun$\gtrsim10.5$, it would increase
pre-JWST number densities at $z>7$ by up to a factor $\sim$60. Similarly, if
they are OSOs with luminosities in the L$_{\rm bol}>10^{46-47}$ erg s$^{-1}$
range, their number would exceed that of bright blue QSOs by more than two
orders of magnitude. Additional photometry at mid-IR wavelengths will reveal
the true nature of the red continuum emission in these EROs and will place this
puzzling population in the right context of galaxy evolution.
