The archbishop of New York on Sunday agreed that Republican presidential candidate Rick Santorum had a “good point” when he said that John F. Kennedy’s speech about the separation of church in state made him want to “throw up.”

In a 1960 speech, Kennedy had assured Southern Baptist leaders that as the nation’s first Catholic president, he would not take orders from the Pope.

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Earlier this year, Santorum told ABC News that Kennedy’s words made him inclined to vomit.

“To say people of faith have no role in the public square, you bet that makes you throw up,” the candidate insisted. “What kind of country do we live in that says only people of non-faith can come in the public square and make their case.”

“That makes me throw up and it should make every American,” Santorum added.

During an Easter Sunday interview, CBS host Bob Schieffer asked Cardinal Timothy Dolan if there should be a separation of church and state.

“You bet there should,” Dolan asserted. “I find myself, believe it or not, agreeing with both of them. I would cheer what John Kennedy said. He was right. And I would find myself among those applauding that speech.”

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“That having been said, I would also say that Sen. Santorum had a good point,” he continued. “Unfortunately what John Kennedy said in September of 1960 to the Baptist Ministerial Alliance in Texas has been misinterpreted to mean a separation of church and state also means a cleavage, a wall between one’s faith and one’s political decisions, between one’s moral focus and between the way one might act in the political sphere. I don’t think John Kennedy meant that.”

Dolan also told Schieffer that there was not too much religion in politics today.

“I think politics, just like business, just like education, just like arts, just like culture only benefits when religion, when morals and faith has a place there,” he said.

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But when it came to the Obama administration’s decision that all health insurance — include those plans provided by religious institutions — cover contraception for women, Dolan felt that the government had gone too far.

“We’re still worried not just about our institutions, but also the individuals,” Dolan explained. “So, we still find ourselves in a very tough spot. And we’re still going to continue to express what we believe is just not a religious point of view, but a constitutional point of view that America is at her best when the government doesn’t force a citizen or a group of citizens in a religious creed to violate their deepest held moral convictions.”

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Watch the video below from CBS’s Face the Nation, broadcast on April 8, 2012.