  We analyze the Type II Plateau supernovae (SN II-P) 2005cs and 2006bp with
the non-LTE model atmosphere code CMFGEN. We fit 13 spectra in the first month
for SN 2005cs and 18 for SN 2006bp. {\sl Swift} ultraviolet photometry and
ground-based optical photometry calibrate each spectrum. Our analysis shows
both objects were discovered less than 3 days after they exploded, making these
the earliest SN II-P spectra ever studied. They reveal broad and very weak
lines from highly-ionized fast ejecta with an extremely steep density profile.
We identify He{\sc ii} 4686\AA emission in the SN 2006bp ejecta. Days later,
the spectra resemble the prototypical Type II-P SN 1999em, which had a
supergiant-like photospheric composition. Despite the association of SN 2005cs
with possible X-ray emission, the emergent UV and optical light comes from the
photosphere, not from circumstellar emission.
  We surmise that the very steep density fall-off we infer at early times may
be a fossil of the combined actions of the shock wave passage and radiation
driving at shock breakout. Based on tailored CMFGEN models, the direct-fitting
technique and the Expanding Photosphere Method both yield distances and
explosion times that agree within a few percent. We derive a distance to NGC
5194, the host of SN 2005cs, of 8.9$\pm$0.5 Mpc and 17.5$\pm$0.8 Mpc for SN
2006bp in NGC 3953. The luminosity of SN 2006bp is 1.5 times that of SN 1999em,
and 6 times that of SN 2005cs. Reliable distances to Type II-P supernovae that
do not depend on a small range in luminosity provide an independent route to
the Hubble Constant and improved constraints on other cosmological parameters.
