Anthony Picarello, general counsel for the U.S. Conference of Catholic Bishops, said Tuesday if the administration wants to "allay concerns, they need to change the policy," CNN reported.
"Nothing less will do," Picarello told CNN. "The bishops aren't going to stop until this is fixed and that means pursuing every legal means [available] to them to fix it."
Churches are exempt from the policy, which is effective Aug.1, and religious institutions opposing contraception have been given a year's extension to comply.
Meanwhile, White House press secretary Jay Carney tried to alleviate worries, saying the administration would use the transition period "to see if the implementation of the policy can be done in a way that allays some of those concerns."
Carney said during the media briefing Tuesday President Obama's focus is trying to balance the ability of employees of Catholic affiliated employers to get contraception while respecting religious beliefs and convictions.
"We understand the religious concerns here. That is why this balance was sought," Carney said during the regular media briefing. "That's why the process going forward includes a transition period where this discussion will continue to see if there can be ways found that ensure that women get access to these preventive services and that those services are covered -- as they will be for all other women -- and that also takes into account these religious concerns."
Carney said there were exemptions for churches and houses of worship, where it was more a matter of hiring people of like faith, rather than larger institutions, such as hospitals or universities, where "you are going to have folks of all faiths."
The rule, Carney stressed, doesn't require an individual or institution to provide contraception, but requires "coverage for women who work there of different faiths, or of any faith."
Supporters of the provision said they'll go against the church and back the rights of employees at Catholic entities to have birth control and other services paid for by their employers.
"The Catholic hierarchy seems to be playing a cynical game of chicken and they don't seem to care that the health and well-being of millions of American woman are what's at stake here," National Abortion Rights Action League President Andrea Miller told WCBS-TV, New York.
WCBS said it was told U.S. bishops were considering a march on Washington, bringing in people from across the country to protest the law.
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