  In a large class of models we show that the light scalar field responsible
for the Sommerfeld enhancement in the annihilation of dark matter leads to
observable direct detection rates, due to its mixing with the standard model
Higgs. As a result the large annihilation cross-section of dark matter at
present epoch, required to explain the observed cosmic ray anomalies, can be
strongly constrained by direct searches. In particular Sommerfeld boost factors
of order of a few hundred are already out of the CDMS-II upper bound at 90%
confidence level for reasonable values of the model parameters.
