  Recently the second author introduced combinatorial principles that
characterize supercompactness for inaccessible cardinals but can also hold true
for small cardinals. We prove that the proper forcing axiom PFA implies these
principles hold for $\omega_2$. Using this, we argue to show that any of the
known methods for forcing models of PFA from a large cardinal assumption
requires a strongly compact cardinal. If one forces PFA using a proper forcing,
then we get the optimal result that a supercompact cardinal is necessary.
