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.