  We analyze the constraints imposed by Higgs vacuum stability on models with
new fermions beyond the Standard Model. We focus on the phenomenology of Higgs
couplings accessible at the Large Hadron Collider. New fermions that affect
Higgs couplings lead to vacuum instability of the Higgs potential. Above the
scale of vacuum instability, bosonic states must stabilize the potential,
implying a cut-off to the pure fermion model. Conservatively tuning the models
to produce the maximal cut-off for a given Higgs coupling effect, we show that
observing a deviation in the $Htt$, $H$-diphoton, or $H$-digluon coupling,
larger than 20$%$, would require that new bosons exist in order to stabilize
the Higgs potential below about 100 TeV. For generic parameter configurations,
and unless the new fermions are made as light as they can possibly be given
current experimental constraints, observing a 10$%$ deviation in any of these
couplings would suggest an instability cut-off below 10-100 TeV. Similarly, if
new bosons are absent up to a high scale, then a deviation in the $Hbb$ or
$H\tau\tau$ coupling, larger than about 20$%$, should be accompanied by a
sizable deviation in the $Zbb$ or $Z\tau\tau$ couplings that can be
conclusively tested with electroweak precision measurements at planned lepton
colliders.
