Cardinal Timothy Dolan, the archbishop of New York, said Sunday the Catholic church remains opposed to ObamaCare in large part because it requires businesses to offer health-insurance plans that include no-cost contraception.

Dolan, the former president of the U.S. Conference of Catholic Bishops, said the church’s position is a difficult one, considering it has supported universal, affordable and comprehensive health care since the early 1990s.

“We bishops have really been in kind of a tough place,” Dolan said on NBC’s “Meet the Press.” "That's how far we go in this battle. We're not Johnny-come-latelies."

He also warned President Obama that the contraception mandate in his signature health care law might “push aside” some of his biggest supporters.

“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,” said Dolan, several days after the Supreme Court agreed to hear a challenge to the mandate by the Christian-owned retail chain Hobby Lobby.

Dolan also said he was “disappointed” that Congress has failed to pass immigration reform and put the blame on the Republican-led House that has yet to vote on the issue.

“You guys have got to get your act together,” he said. “We’re not going to let you guys off the hook. … We’re disappointed.”

Dolan also acknowledged that efforts to make same-sex marriage legal across the country appear to be gaining momentum.

"I think I'd be a Pollyanna to say there doesn't seem to be kind of a stampede to do this," he said. "I regret that."

He also suggested the church has been “out marketed” on the issue by forces such as Hollywood and high-profile political leaders who support the change.