President Obama’s efforts last week have failed to quell the fury over his decision to require most health plans to cover contraception. Republicans are still promising a fight in Congress, and two leading Catholic groups remain on the fence although the administration thought they had been won over.

In response to outrage from Catholic and other religious groups, Mr. Obama said Friday that he would revise the policy to exempt religiously affiliated employers from buying plans that provide free contraception to employees, but he said insurance companies still would have to provide coverage.

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