UPDATED 02/10/12 11:20 a.m.

CHICAGO (CBS) — Francis Cardinal George came out with guns blazing against a federal rule that would require employers to pay for contraception for their staff, but President Barack Obama has now announced changes to the rule.

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Administration officials say religious employers will not have to pay for birth control for their employees after all, and instead, insurance companies will have to provide free contraception if a religious-based employer objects.

“No woman’s health should depend on who she is, or where she works, or how much money she makes,” President Obama said.

But he pointed out that he started out working with Catholic parishes in poor neighborhoods in Chicago and knows the important work they do, and acknowledged that churches might believe their religious freedom was being violated by the rule.

But he said the purpose of the change in the rule was to move ahead with providing health care to women in the face of “cynical” people who wanted to turn the issue into a “political football.”

On Thursday, the cardinal issued a letter, in which he said the rule that had been set to take effect next year “strikes at the fundamental right to religious liberty and for all citizens of any faith.”

The rule would have required religious-based hospitals, schools and charities that employ non-Catholics to pay for “all FDA-approved forms of contraception” for employees. The rule never applied to churches or other explicitly religious-affiliated employers.

The since-modified rule was issued by the U.S. Department of Health and Human Services on a recommendation by an arm of the arm of the National Academy of Sciences. The academy considers access to birth control improves maternal and infant mortality rates.

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But the cardinal said the earlier rule presented Roman Catholics with the choice of either to “violate our consciences, or drop health care coverage for our employees (and suffer the penalties for doing so.)”

Cardinal George went on to characterize the earlier rule as an attack on religious people.

“People of faith cannot be made second class citizens because of their religious beliefs,” George wrote. “We are already joined by our brothers and sisters of all faiths and many others of good will in this important effort to regain our religious freedom. Our parents and grandparents did not come to these shores to help build America’s cities and towns, its infrastructure and institutions, its enterprise and culture, only to have their posterity stripped of their God-given rights.”

He added that the earlier rule “reduces the church to a private club, destroying her public mission in society.”

The cardinal wrote that the earlier rule and its implications for religious liberty warranted “prayer and fasting that wisdom and justice may prevail, and religious liberty may be restored.”

Cardinal George had not issued any new statements in the wake of the changes to the rule as of 11 a.m.

The teachings of the Catholic Church dictate that birth control is never acceptable under any circumstances.

The Catechism of the Catholic Church states the teaching thusly: “Every action which, whether in anticipation of the conjugal act, or in its accomplishment, or in the development of its natural consequences, proposes, whether as an end or as a means, to render procreation impossible is intrinsically evil.”

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But a poll by the Public Research Institute says a slim majority of Americans – including Roman Catholics – believe employers should be required to pay for contraception for their employees, CBS News reported.