  We study Higgs boson couplings in the large-$\lambda$ version of the
Next-to-Minimal Supersymmetric Standard Model, known as $\lambda$-SUSY. We find
that the predicted deviations from the Standard Model (SM) in these couplings
are inversely correlated with the amount of fine-tuning needed to accommodate a
126 GeV Higgs. In the most natural regions of parameter space, the 126 GeV
Higgs has large admixtures of both the SM-singlet and the non-SM Higgs doublet
scalars, and such regions are already ruled out by the LHC. Future improvements
in the Higgs coupling measurements will either discover deviations from the SM,
or put further stress on naturalness in $\lambda$-SUSY.
