Dallas ? In unprecedented sessions described as “heartbreaking” by one church leader, victims of clerical sex abuse shared their personal stories with Roman Catholic bishops Wednesday, the eve of a critical meeting on disciplining abusive priests.

The two sides emerged from the private gatherings for a dramatic news conference, in which victims and U.S. cardinals sat side-by-side and spoke about the church’s past protection of errant clergy. About 20 victims participated in the meetings along with about a dozen clergymen.

Mark Serrano, of the Survivors Network of Those Abused by Priests, held up a picture of himself at age 12 and told of how he was raped by a priest. He then urged the bishops to adopt a national abuse policy under which church leaders not just abusive priests would “be fired or defrocked” for failing to protect young people. Bishops generally haven’t supported that idea.

“Listening comes easy,” said Serrano, now 38. “Talk comes cheap. Moral action is priceless.”

Cardinal Theodore McCarrick of Washington, D.C., said he found the sessions “heartbreaking.”

“I think it touched us all deeply to see how so many people had suffered because of a few sick and very mixed up priests, criminal priests,” he said. “In the last couple of hours, I hope I’ve grown. I hope I will be wiser and more courageous when the committee presents its report.”

Victims have met previously with church leaders over the years, both individually and in groups. But never has so much been at stake.

The aim of the U.S. bishops’ meeting starting today is to adopt a policy for handling abuse claims that will finally ease the torrent of molestation accusations that have plagued the American church.

Since January, when the crisis began with the case of a pedophile clergyman in Boston, at least 250 of the nation’s 46,000 priests have resigned or been suspended over sexual misconduct claims. Four bishops also have resigned, but none have left their post because they mishandled abusive clergy.

David Clohessy, SNAP’s national director, said members of his group spent most of their two hours with church leaders pressing for some mechanism to discipline bishops who fail to comply with whatever national policy is approved. But he said the bishops made no promises on their request.

The victims are competing for influence with the many U.S. prelates who have suggested amendments to a draft of the policy, which the Ad Hoc Committee on Sexual Abuse made public last week. The document included input from at least one victim.

Archbishop Harry Flynn, the committee chairman, is working through 107 pages of amendments and said he anticipated “substantial modifications” to the draft plan.

Bishop Wilton Gregory, president of the United States Conference of Catholic Bishops, said the document was meant to heal a rift with Catholics angered by the scandal, although he did not expect the crisis to be resolved when the meeting ends Saturday.

“Dallas has to be a first step, a significant first step in restoring the credibility of the bishops,” he said. “Our people have to be able to say, ‘They get it.”‘

A key issue is whether to adopt zero tolerance for all abusers specifically whether to allow priests who molested one minor in the past, but no more than that, to stay in the clergy under tight restrictions.

Cardinal Roger Mahony of Los Angeles said he has concluded from conversations with fellow bishops that the final policy approved Friday will most likely force out all abusers, including those with only one offense.

“We’ve got to come out of here with very strong zero tolerance past, present and future,” Mahony said.

Two new polls, one by ABC News and the other released Wednesday by Quinnipiac University, each found more than 80 percent of American Catholics back Mahony’s position.