  The $Z_{2}$-symmetric version of the Georgi-Machacek model does not possess a
decoupling limit in which all the new particles can be made arbitrarily heavy,
opening the possibility that the model can be entirely excluded if experiments
reveal no deviations from the Standard Model. We explore this model, focusing
on the part of parameter space in which the vacuum expectation value of the
triplets, $\nu_\chi$, is small. In the small-$\nu_\chi$ limit, the second
custodial-singlet scalar field $S$ necessarily becomes very light and can
contribute to the total width of the 125 GeV Higgs boson $h$ via $h \to SS$. We
show that this process, together with LHC measurements of the $h \to
\gamma\gamma$ rate, entirely excludes masses $m_S < m_h/2$ and thereby severely
constrains the parameter space, setting an experimental lower bound $\nu_\chi
\gtrsim 12.5$ GeV on the vacuum expectation value of the triplets. This lower
bound makes it impossible to avoid deviations from the Standard Model in the
couplings of $h$ to fermion and vector boson pairs. We study the remaining
parameter space after imposing constraints from direct searches for the
additional Higgs bosons, and show that it is on the edge of being fully
excluded at $95\%$ confidence level by LHC measurements of the 125 GeV Higgs
boson's couplings. Measurements of these couplings at the future
high-luminosity run of the LHC will have sufficient precision to entirely
exclude the model at $5\sigma$ if no deviations from the Standard Model are
observed.
