  We calculate the tidal response of helium and carbon/oxygen (C/O) white dwarf
(WD) binaries inspiraling due to gravitational wave emission. We show that
resonance locks, previously considered in binaries with an early-type star,
occur universally in WD binaries. In a resonance lock, the orbital and spin
frequencies evolve in lockstep, so that the tidal forcing frequency is
approximately constant and a particular normal mode remains resonant, producing
efficient tidal dissipation and nearly synchronous rotation. We show that
analogous locks between the spin and orbital frequencies can occur not only
with global standing modes, but even when damping is so efficient that the
resonant tidal response becomes a traveling wave. We derive simple analytic
formulas for the tidal quality factor Q and tidal heating rate during a g-mode
resonance lock, and verify our results numerically. We find that Q ~ 10^7 for
orbital periods ~ 1 - 2 hr in C/O WDs, and Q ~ 10^9 for P_orb ~ 3 - 10 hr in
helium WDs. Typically tidal heating occurs sufficiently close to the surface
that the energy should be observable as surface emission. Moreover, near an
orbital period of ~ 10 min, the tidal heating rate reaches ~ 10^{-2} L_\sun,
rivaling the luminosities of our fiducial WD models. Recent observations of the
13-minute double-WD binary J0651 are roughly consistent with our theoretical
predictions. Tides naturally tend to generate differential rotation; however,
we show that the fossil magnetic field strength of a typical WD can maintain
solid-body rotation down to at least P_orb ~ 10 min even in the presence of a
tidal torque concentrated near the WD surface.
