Hybrid meson energies are calculated in the static quark limit with the Dyn
amical Quark Model (DQM). In the DQM, transverse gluons are represented as
effective constituents with a dynamically generated mass. Hybrid masses are
determined within the Tamm-Dancoff approximation for the resulting relativ
istic Salpeter equation. Although the general features of the adiabatic pot
ential surfaces correspond with lattice data, the results disagree on level
orderings. Similar problems appear to exist in all constituent glue models
of hybrids. We conclude that constituent gluons do not accurately represen
t soft gluonic degrees of freedom.