  We consider fluctuations in a perfect irrotational fluid coupled to gravity
in an Einstein static universe background. We show that the homogeneous linear
perturbations of the scalar and metric fluctuations in the Einstein static
universe must be present if the second order constraint equations are to be
integrable. I.e., the 'linearization stability' constraint forces the presence
of these homogeneous modes. Since these linear homogeneous scalar modes are
well known to be exponentially unstable, the tactic of neglecting these modes
to create a long-lived, almost Einstein universe does not work, even if all
higher order (L $>$ 1) modes are dynamically stable.
