Under fire from prominent Catholic groups, President Obama will revise a rule his administration created last month that would have required Catholic universities and hospitals to offer their workers health insurance plans that include birth control.

The new policy, which White House officials announced early Friday, will instead allow religious institutions to offer insurance without contraceptive coverage, but health insurance companies would be required to provide free contraceptive coverage for people who want it.

The shift comes after a barrage of criticism from not only Republicans but even some liberal Catholics who argued the original Obama administration policy was an intervention into religious freedom.

The rule, part of the implementation of the new health care law, already exempted churches from the contraceptive requirement. But Catholic groups in particularly still sharply opposed it, arguing it would require them to offer health insurance plans against their religious beliefs.

Black religious leaders have said little about the controversy, and some other religious groups have actually defended the president. But the last week has seen an unusual political alliance, from liberal Catholics such as Washington Post columnist E.J. Dionne and Sen. John Kerry (Mass) to as conservative Republicans like Rick Santorum all suggesting the rule needed to be revised.

The White House had long anticipated the controversy, which in effect pitted women’s rights groups, who strongly support expanding access to contraception, against Catholic bishops and activists. But the administration appears not to have anticipated the sustained controversy over the issue and numerous congressional Democrats abandoning Obama on the issue.

In its compromise, Obama is trying to appease all sides. Some women’s groups have already spoken out in favor of the compromise, but it’s not yet clear if Catholic bishops will do the same.

“We believe the compliance mechanism does not compromise a woman’s ability to access these critical birth control benefits,” said Cecile Richards, president of Planned Parenthood, in a statement defending the new policy.

Sister Carol Keehan, the president of the Catholic Health Association, which represents Catholic hospitals, also praised new rule.

“The Catholic Health Association is very pleased with the White House announcement that a resolution has been reached that protects the religious liberty and conscience rights of Catholic institutions,” Keehan said in a statement.

It’s unclear if this issue will have any political impact. Republicans have galvanized around this issue as what they call another example of the continued ” assault on religion” by the Obama administration, but the activists making those statements likely would have voted against the president in November no matter what.

Catholics don’t traditionally vote as a bloc, but many swing voters in key states like Michigan are Catholic, and Obama’s reelection team must take them into account in its strategy.

The contraceptive requirements go into effect in August of 2012.

Follow Perry Bacon Jr. on Twitter at @perrybaconjr