  I study the effect of Coulomb interaction on superconducting order in a
d-wave lattice superconductor at T=0 by considering the superconducting saddle
point in the two dimensional t-J-U model with an on-site repulsion U. The
theory of low energy phase fluctuations around this saddle point is derived in
terms of the effective hard-core bosons (representing the density of spin-up
electrons and the order parameter phase), interacting with the fluctuating
density of spin-down electrons. Whereas the saddle point value of the gap is
found to monotonically increase towards half filling, the phase stiffness at
T=0 has a maximum, and then decreases with further underdoping. Right at half
filling the stiffness vanishes for large U.
  This argues that the pseudogap phenomenon of the type observed in cuprates is
in principle possible without a development of any competing order, purely as a
result of growing correlations in the superconducting state. The effects of
finite temperature and disorder are discussed qualitatively.
