New York Cardinal Timothy Dolan said on Friday that the Catholic Church could have been one of Obamacare's "biggest cheerleaders" if it wasn't for the law's contraception mandate. 

Dolan, who just finished his term as chairman of the U.S. Conference of Catholic Bishops, said in an interview with "Meet the Press" that some of the stipulations in the Affordable Care Act prevent the church from fully embracing the law, NBC News reports. 

"We've been asking for reform in healthcare for a long time.  So we were kind of an early supporter in this," Dolan said in the interview, which will air on Sunday. "Where we started bristling and saying, 'Uh-oh, first of all this isn't comprehensive, because it's excluding the undocumented immigrant and it's excluding the unborn baby,' so we began to bristle at that."

Catholic leaders have been particularly concerned about the law's requirement which mandates that employers and health care providers provide female employees access to contraceptive and family-planning services. Catholic teaching is opposed to abortion rights and the use of contraception. 

Obama has tried to circumvent the issue by allowing employers to opt out of providing coverage for birth control, but requiring insurers to explain the option directly to consumers whose employers refuse to cover birth control because of moral concerns. 

"So that's when we began to worry and draw back and say, 'Mr. President, please, you're really kind of pushing aside some of your greatest supporters here. We want to be with you, we want to be strong.  And if you keep doing this, we're not going to be able to be one of your cheerleaders,'" Dolan said. "And that sadly is what happened."

Dolan also spoke on the topic of same-sex marriage, Fox News reports. 

"I think maybe we've been out-marketed, sometimes.  We've been caricatured as being anti-gay," Dolan said. "When you have forces like Hollywood, when you have forces like politicians, when you have forces like some opinion-molders that are behind it, it's a tough battle."

Dolan said the church is "not going to give up" on traditional marriage.