President Barack Obama needs to find a new envoy to the Vatican since Ambassador Miguel Diaz, appointed in 2009, has accepted a position as professor of faith and culture at the University of Dayton in Ohio. Obama's choice for a replacement is being closely watched in Rome, according to one senior Vatican diplomat, because it signals what kind of relationship Obama wants to have during his second term.

Filling the slot tends to be a special headache for Democratic presidents because they have to find somebody who can pass muster both with their party and with the Vatican. The custom that it has to be a Catholic complicates things further, because it's not just a candidate's policy positions that might cause problems, but his or her internal standing in the...