WASHINGTON — For the White House, the decision announced Friday to soften a rule requiring religious-affiliated organizations to pay for insurance plans that offer free birth control was never really driven by a desire to mollify Roman Catholic bishops, who were strongly opposed to the plan.

Rather, the fight was for Sister Carol Keehan — head of an influential Catholic hospital group, who had supported President Obama’s health care law — and Catholic allies of the White House seen as the religious left. Sister Keehan had told the White House that the new rule, part of the health care law, went too far.

“I felt like he had made a really bad decision, and I told him that,” Sister Keehan said of the president. “I told his staff that. I felt like they had made a bad decision on principle, and politically it was a bad decision. For me another key thing was that it had the potential to threaten the future of health reform.”

Mr. Obama announced that rather than requiring religiously affiliated charities and universities to pay for contraceptives for their employees, the cost would be shifted to health insurance companies. The initial rule caused a political uproar among some Catholics and others who portrayed it as an attack on religious freedom.

Meeting with his top advisers in the Oval Office last week amid rising anger from Catholic Democrats, liberal columnists and left-leaning religious leaders — a fed-up Mr. Obama issued an order meant for Kathleen Sebelius, the secretary of health and human services. Ms. Sebelius and agency lawyers had initially told the president they needed a year to work out a compromise that had seemed obvious to some in the administration from the start: make the new rule more like that offered by the State of Hawaii, where employees of religiously affiliated institutions obtained contraceptives through a side benefit offered by insurance companies.

But in difficult internal negotiations, a group of advisers had bested Vice President Joseph R. Biden Jr. and others and sold the president on a stricter rule. Now the political furor surrounding it was threatening to consume signs of economic improvement giving a boost to the White House and put the Obama re-election campaign on the defensive.

Time was up, Mr. Obama told his advisers, according to officials in the meeting. Ms. Sebelius, a Catholic who, along with the president’s senior adviser Valerie Jarrett and domestic policy adviser Melody Barnes, had pushed hard for the new rule, was not there, but the message came through: Figure out a way to make something like the Hawaii model work.

In announcing the shift on Friday, Mr. Obama sought to quell the brewing rebellion. Not unexpectedly, the Catholic bishops issued a statement renewing their call for “legislative action on religious liberty,” and calling rescission of the mandate the “only complete solution.” And Speaker John A. Boehner’s spokesman on Friday promised that House Republicans “will continue to work toward a legislative solution.”

What had not been anticipated enough, despite warnings from Mr. Biden; the former chief of staff William Daley; Mr. Biden’s chief of staff, Bruce Reed; and the deputy national security adviser Denis McDonough, administration officials said, was that allies would be furious, too.

Tim Kaine, a Virginia Senate candidate and former head of the Democratic National Committee, echoed the concern of Sister Keehan, president of the Catholic Health Association, that it went too far. So did some liberal-leaning Catholics in the news media, like Chris Matthews of MSNBC’s “Hardball,” who called the rule “frightening,” and E. J. Dionne, the Washington Post columnist, who wrote that Mr. Obama had “utterly botched” the issue.

Meanwhile, Sister Simone Campbell, executive director of Network, a group founded by nuns decades ago to lobby on social justice issues, warned White House officials that nearly 500 Catholic activists would be in Washington this weekend for a conference, and that if no compromise had been reached by then, all of them would return to their parishes fired up about the contraception mandate.

“We were getting killed,” one administration official said Friday. The White House picked the deputy chief of staff Nancy-Ann DeParle to talk to Sister Keehan about ways the rule could be made palatable. Meanwhile, administration officials were hearing from women’s rights organizations, particularly Planned Parenthood, who warned that they would oppose any compromise that made employees pick up the tab.

“After the many genuine concerns that have been raised over the last few weeks, as well as, frankly, the more cynical desire on the part of some to make this into a political football, it became clear that spending months hammering out a solution was not going to be an option,” Mr. Obama said on Friday.

Some who favor the compromise wonder why it took so long. “What has happened a few times in this administration is that they get so focused on the substantive policy, they get kind of narrowly focused and lose sight of the countervailing concerns,” Sister Campbell said.

At the White House, the internal debate had raged since last fall, when administration officials started looking at how to put the rule into practice. All agreed early on that churches would be exempt. The question revolved around colleges, charities and other religiously affiliated institutions that employed people of different faiths.

Archbishop Timothy M. Dolan of New York met with Mr. Obama and argued in favor of a broad exemption. Shortly after, Cecile Richards, president of Planned Parenthood, and other proponents of the rule began a series of meetings with officials to argue against an exemption for religiously affiliated institutions.

Throughout that debate, administration officials said, Mr. Obama pushed hard for a version of the Hawaii rule. But Ms. Sebelius and others at the Department of Health and Human Services said it would take time to resolve whether the administration could emulate that approach. In the end, with the State of the Union address imminent and time passing to work out the new rules governing the carrying out of the health care law, the administration announced on Jan. 20 that religious-affiliated institutions — but not churches — would have to offer the insurance.

“All hell broke loose,” one administration official said, leading to Mr. Obama’s sharp orders in the Oval Office last week.

The result differs from Hawaii in that it shifts the cost to insurers, instead of employees. It also differs from Hawaii in that it requires companies — and not the religious institutions —  to inform employees about how to arrange coverage.

Before making his announcement, Mr. Obama on Friday called three people: Sister Keehan, Ms. Richards and Archbishop Dolan. From Sister Keehan and Ms. Richards, he got unqualified endorsements. Even the archbishop offered, initially, a grudging acknowledgment that it was “a first step in the right direction” — although the bishops later said that Mr. Obama’s fix “raises serious moral concerns.”

Helene Cooper reported from Washington, and Laurie Goodstein from New York.