Since the United States and the Vatican established full diplomatic ties in 1984, little attention has been paid to the process and politics of selecting a U.S. ambassador to the Holy See. That's changing under a new president whose positions have been criticized by several American bishops and conservative Catholics.

The Obama administration's search to fill the vacant position is anticipated to bring a level of scrutiny unmatched since the very prospect of diplomacy with the Vatican stirred American fears of papal loyalists swearing allegiance to church over country.

While Middle East peace, U.S. troops in Iraq and Afghanistan and relations with the Muslim world loom as shared interests for the military superpower and the religious superpower, the politics of abortion hangs over the process.

President Obama's support of abortion rights, at odds with Catholic church teaching, has been divisive among U.S. Catholics. The issue has taken on greater prominence since the University of Notre Dame invited Obama to speak at its commencement and receive an honorary law degree next month. At least 32 U.S. bishops have spoken out against the decision by the nation's flagship Catholic university.

Against that backdrop, the Obama administration must weigh any candidate's abortion stance, decide whether to pick a Catholic or non-Catholic, and whether to go with a career diplomat or a political appointment. Another factor: the Holy See, like any host country, can reject a name for any reason.

Vatican spokesman the Rev. Federico Lombardi said this week that the Obama administration has not submitted names to the Vatican for consideration. He rejected reports in U.S. and European media that names had been floated and rejected. The White House declined to comment on the process or where it stands.

"What that ambassador does is build bridges," said Cathleen Kaveny, a Notre Dame law and theology professor who served on the Obama campaign's Catholic advisory committee. "The ideal candidate could build bridges between the administration and the Holy See. There's a lot they have in common — social justice, human rights. There are a lot of things they don't hold in common, but a lot they can work on together."

All eight U.S. ambassadors to the Holy See have been Catholics who oppose abortion rights. Former Boston Mayor Raymond Flynn, a Democrat who held the position in the Clinton administration, and others say the next ambassador doesn't have to be Catholic — although critics would likely seize on a non-Catholic as evidence that no Catholic Democrat was suitable.