The recent detection of polarized radiation from Sgr A* requires a
non-thermal electron distribution for the emitting plasma. The Faraday rotation
measure must be small, placing strong limits on the density and magnetic field
strength. We show that these constraints rule out advection-dominated accretion
flow models. We construct a simple two-component model which can reproduce both
the radio to mm spectrum and the polarization. This model predicts that the
polarization should rise to nearly 100% at shorter wavelengths. The first
component, possibly a black-hole powered jet, is compact, low density, and
self-absorbed near 1 mm with ordered magnetic field, relativistic Alfven speed,
and a non-thermal electron distribution. The second component is poorly
constrained, but may be a convection-dominated accretion flow with dM/dt~10^-9
M_Sun/yr, in which feedback from accretion onto the black hole suppresses the
accretion rate at large radii. The black hole shadow should be detectable with
sub-mm VLBI.Comment: 4 pages, 1 figure, accepted by ApJL, several changes from submitted
versio