As word trickled out of a White House compromise with Catholic groups on its rule around contraception coverage on Friday morning, administration officials took to the phones to sell the plan to religious leaders across the spectrum.

Catholic officials say President Obama called New York Archbishop Timothy Dolan, President of the US Conference of Catholic Bishops, to explain the revised policy, which exempts religiously affiliated universities and hospitals for paying for no cost contraception for their employees but requires insurers to offer such coverage for for free to women who work at such institutions.

Dolan responded to the White House plan Friday afternoon in a statement saying the move was, "a first step in the right direction."

"While there may be an openness to respond to some of our concerns, we reserve judgment on the details until we have them," he added.

But other bishops were far more critical. "I think he's punting, just kicking the can down the road," Miami Archbishop Thomas Wenkis told CNN. "He's hasn't really addressed our concerns. I think the only thing to do is... to take back the whole thing."

After hanging up with Obama Friday morning, Dolan quickly organized a conference call with other bishops nationwide, according to a source briefed on the calls. It's yet to be seen how the Catholic Church will greet the revised White House policy, but some conservative religious voices say they're not satisfied.

Wenkis said the Miami Archdiocese pays an insurance company to cover its 5,000 employees and argued that if the insurance company is paying for and providing contraceptives, as the new compromise lays out, the church would still be paying for it.

"They're missing the point when they say this is about contraception," he said. "This is about religious freedom. It's a sham to say contraception aren't widely available in this country."

But some Catholic groups applauded the White House announcement. Sister Carol Keehan from the Catholic Health Association said she is"very pleased" with the White House.

"Folks were extremely grateful for this," said James Salt, who heads the progressive group Catholics United, which is close to the White House.

Salt was on a White House call to religious leaders Friday morning that was led by Joshua DuBios, director of Obama's Office of Faith-based and Neighborhood Partnerships.

"This is a solution that can be universally celebrated," Salt said. " There were groups on the call that have a very pro-choice world view and there was no dissent... We're putting out a full-throated endorsement of this."

Stephen Schneck, a professor from Catholic University who has advised the administration in the past, is also pleased with the new HHS policy. "There was great enthusiasm on the call, a real sense of relief," he said, referring to the conference call with DuBois.

"I think [the administration] finally got it as a result of the fire storm...the religious liberty concerns, that's what turned the policy makers," he said. "The level of solidarity with the bishops in seeing this as a religious liberty issue is what I think turned the day."

In recent weeks, religious leaders loudly lobbied the White House on its plan to make religious institutions offer free contraception to employees through health insurance plans. Evangelicals and conservative Jews joined with Catholics in saying the policy was an intrusion of religious liberty.

"As long as the Obama portrayed this as a contraception issue they had a chance to win the pr battle," said Richard Land, head of public policy for the Southern Baptist Convention. Despite the compromise, Land said the damage has been done.

"It'll be devastating with Catholics," he said, arguing that the president has "shown what he really believes."

The Becket Fund for Religious Liberty, which brought three lawsuits in federal court against the policy, denounced the White House change Friday as an "accounting gimmick."

Becket said the new compromise doesn't address the private religious groups and others who object the policy and still view the new policy as them paying for contraceptives, albeit through an insurer.

"Hundreds, if not thousands, of religious institutions are still left out in the cold and will be forced to violate their religious convictions," said Hannah Smith, senior legal counsel for the Becket Fund, in a statement.

An administration official said the White House will convene meetings with religious leaders in coming days and that "this policy will be developed collaboratively so that the ultimate outcome works for religious employers, their workers and the public."