  Using experimental spectral data for hadronic tau decays from the OPAL
experiment, supplemented by a phenomenologically successful parameterization
for the high-s region not covered by the data, we construct a physically
constrained model of the isospin-one vector-channel polarization function.
Having such a model as a function of Euclidean momentum Q^2 allows us to
explore the systematic error associated with fits to the Q^2 dependence of
lattice data for the hadronic electromagnetic current polarization function
which have been used in attempts to compute the leading order hadronic
contribution, a_\mu^HLO, to the muon anomalous magnetic moment. In contrast to
recent claims made in the literature, we find that a final error in this
quantity of the order of a few percent does not appear possible with current
lattice data, given the present lack of precision in the determination of the
vacuum polarization at low Q^2. We also find that fits to the vacuum
polarization using fit functions based on Vector Meson Dominance are
unreliable, in that the fit error on a_\mu^HLO is typically much smaller than
the difference between the value obtained from the fit and the exact model
value. The use of a sequence of Pade approximants known to converge to the true
vacuum polarization appears to represent a more promising approach.
