  Some short-period exoplanets (hot Jupiters) are observed by their transits to
have anomalously large radii. It has been suggested that these planets are in a
resonance involving persistent misalignment and synchronous precession of their
spin and orbital angular momenta, a Cassini state, and that the attendant tidal
heating inflates the planet. We argue against this. Using explicit tidal
integrations, we show that although an oblique Cassini state can dissipate many
times the rotational energy of the planet, the rate of dissipation must be much
less than hypothesized. Dissipation causes the planetary spin to lie at an
angle to the plane containing the orbital and total angular momenta. If
dissipation is too rapid, this angle becomes so large that Cassini equilibrium
is lost. A separate consideration limits the total energy that can be extracted
from the orbit. The source of the torque on the orbit, either an oblique parent
star or an inclined third body, aligns with the orbit as it absorbs the angular
momentum shed by the planet. Alignment removes the orbital precession required
by the Cassini state. In combination with observational bounds on the mass and
semimajor axis of a possible second planet and with bounds on the stellar
rotation and obliquity, these constraints make it very unlikely that obliquity
tides can be the explanation for inflated hot Jupiters, especially HD 209458b.
