  CSS1603+19 is a cataclysmic variable (CV) with an orbital period of 81.96
min, near the minimal period of cataclysmic variables. It is unusual in having
a strong mid-infrared excess inconsistent with thermal emission from a brown
dwarf companion. Here we present time-resolved multi-wavelength observations of
this system. WISE photometry indicates that the mid-infrared excess displays a
one-magnitude eclipsing-like variability during the orbit. We obtained
near-infrared and optical spectroscopy using Gemini, MDM and APO telescopes.
Near-infrared spectra show possible cyclotron features indicating that the
white dwarf has a magnetic field of about 5MG. Optical and near-infrared
spectra display double-peaked emission lines, with both components showing
strong radial velocity variations during the orbital period and with the broad
component leading the narrow component stably by about 0.2 of the orbital
phase. We construct a physical model informed by existing observations of the
system and determine that one component likely originates from the accretion
column onto the magnetized white dwarf in synchronous rotation with the orbital
motion and the other from the Roche overflow point. This allows us to constrain
the masses of the binary components to be $M_1>0.24 M_{\odot}$ for the white
dwarf accretor and $M_2=0.0644\pm0.0074 M_\odot$ for the donor. We classify the
system as an AM Herculis star, or a polar. It has likely completed its stint on
the period gap, but has not yet gone through the period bounce.
