The news that New York Cardinal Timothy Dolan, the nation’s most prominent Catholic prelate, will deliver the closing blessing to the Republican National Convention in Florida next week was seen as a huge coup for Mitt Romney, the party’s presumptive nominee. But the move has also prompted a sharp debate within the church over the increasingly close ties between leading bishops and the GOP.

“The cozy relationship between a sizable portion of U.S. bishops and the Republican Party should be cause for concern, and not just among progressive Catholics,” Michael O’Loughlin wrote in a post on the website of America magazine, a leading Catholic weekly published by the Jesuits.

“Cardinal Dolan’s appearance in Tampa will damage the church’s ability to be a moral and legitimate voice for voiceless, as those who view the Catholic Church as being a shill for the GOP have just a bit more evidence to prove their case,” O’Loughlin concluded.

Similarly, David Cruz-Uribe, a member of the Secular Franciscan Order and a professor of mathematics at Trinity College, wrote on the Vox Nova blog that Dolan’s decision “will only drag the Church further into a partisan divide and fuel the perception (true or not) that the Catholic Church wants to replace the Episcopalians as the Republican party on its knees.”

Conservative Catholics have, not surprisingly, welcomed Dolan’s appearance and hope it augurs well for Romney.

“I now predict that if Mitt Romney wins the White House in 2012 there will be a very healthy relationship between a Romney administration and the U.S. Bishops, led by a close working relationship between Cardinal Dolan and President Romney,” said Thomas Peters, who writes for CatholicVote.org, which has endorsed Romney and his Catholic running mate, Paul Ryan.

Romney disclosed the news of Dolan’s planned blessing on Wednesday (Aug. 22) during an interview on the conservative Catholic cable channel EWTN. He did so in the context of a discussion about his shared opposition with the bishops to the Obama administration’s controversial birth control mandate.

By tradition, the local bishop often delivers a prayer at the party convention meeting in his city, but it is highly unusual for another bishop ― and the leader of the hierarchy ― to fly in to deliver a benediction, as Dolan will do on Aug. 30, right after Romney is formally nominated.

Philadelphia’s Cardinal John Krol did so in 1972 when he was president of the bishops’ conference and went to Miami for the Republican convention that nominated Richard Nixon and Spiro Agnew. But that seems to be the only modern precedent.

Whether Dolan’s appearance will have any actual effect in swinging Catholic voters to Romney is unclear. Obama is holding a slim lead among Catholics at this point, and Catholics often ignore the hierarchy’s advice on political matters.

Dolan’s spokesman has sought to portray the cardinal’s appearance as purely nonpartisan: “It’s as a priest going to pray,” said Joseph Zwilling, director of communications for the Archdiocese of New York.

Zwilling reiterated that point in a statement released on Thursday, and added that Dolan “would be willing to accept a similar offer from the Democratic Party as well.”

But the Democrats seem unlikely to extend an invitation to Dolan, who is among dozens of Catholic leaders suing the administration over the contraception mandate. It’s also very possible that Dolan would not receive a warm welcome when the Democrats hold their convention in Charlotte, N.C., a week after the GOP nominates Romney in Tampa, Fla.

Dolan and the bishops have become increasingly critical of Obama as policy differences over gay marriage and abortion rights have provided ammunition for fierce rhetorical blasts from many bishops and their allies, who have compared Obama to a totalitarian dictator, or worse.

Earlier this month, Baltimore Archbishop William P. Lori, an up-and-coming voice in the hierarchy who has led the campaign against the administration’s contraception policy, gave an interview that was widely viewed as indicating that a good Catholic could not vote for a candidate who supports abortion rights, as Obama does.

At the same time, Romney’s selection of Ryan as his running mate has brought an outpouring of praise from several bishops. Some of them like Ryan’s proposals on cutting entitlements and taxes, despite the conflict that other bishops see between those policies and Catholic teaching.

Others, like Dolan, who was archbishop of Milwaukee before coming to New York in 2009, have close personal ties to Ryan, a Wisconsin congressman. Dolan has often taken a softer line on Ryan’s policies than other Catholic leaders, and his praise has grown as Ryan’s visibility has increased.

Dolan recently told a radio program that he is “happy” Ryan is on the GOP ticket and called him a “great public servant.”

“We go way back, Congressman Paul Ryan and I,” Dolan said. “I came to know and admire him immensely. And I would consider him a friend. He and his wife Janna and their three kids have been guests in my house; I’ve been a guest at their house. They’re remarkably upright, refreshing people.”

Ryan’s own bishop, Robert Morlino of the Diocese of Madison, has also emerged as a strong defender of Ryan’s Catholic bona fides.

Morlino wrote a column this month expressing pride in Ryan’s “accomplishments as a native son, and a brother in the faith.” And on Tuesday he told a radio program that Ryan is an “excellent Catholic layman of the very highest integrity” who “understands the principles of Catholic social teaching” and applies them “very responsibly.”

There was at least one bit of good news for Catholic Democrats this week, however. Organizers of next month’s Values Voter Summit in Washington, a major political rally for the religious right, announced that Cardinal Dolan had been invited to speak. But Zwilling said that wouldn’t happen.

“He has not received an invitation as far as we can tell,” Zwilling said. “In any event, he is not going.”