  We study the effect of order parameter phase fluctuations on the
single-particle properties of fermions in the underdoped cuprate
superconductors using a phenomenological low-energy theory. We identify the
fermion-phase field coupling as the Doppler-shift of the quasiparticle spectrum
induced by the fluctuating superfluid velocity and we calculate the effect of
these fluctuations on the fermion self-energy. We show that the vortex pair
unbinding near the superconducting transition causes a significant broadening
in the fermion spectral function, producing a pseudogap-like feature. We also
discuss the specific heat and show that the phase fluctuation effect is visible
due to the short coherence length.
