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The compromise sought to accommodate religious organizations like Catholic hospitals and universities that did not want to be forced to provide free contraceptive coverage to employees.
"We think it is a very good resolution of the problem," Lew said on CNN. "It's gotten the support of a wide range of organizations from Catholic charities and the Catholic Health Association to Planned Parenthood."
But many still oppose it, including the Republican candidates vying to become their party's nominee to face Obama in the Nov. 6 presidential election.
"They're forcing religious organizations, either directly or indirectly, to pay for something that they find is a deeply morally wrong thing and this is not what the government should be doing," Republican candidate Rick Santorum said on NBC's "Meet the Press".
Santorum, a staunch Catholic who has attracted social conservatives in his bid for the White House, said he has no problem with the public policy of allowing women access to contraception.
"The question is whether some religious organization should be forced to pay for something that they believe is a moral wrong," he said. "And the answer to that is no and under the Obama administration policy they are continuing to be forced to do so."
"I see a government that is trying to do too much," Piotrowicz said. "This compromise to me, it seems like a kind of cheap accounting trick. I don't think this compromise is the right move."
Jose Florez, a Boston doctor, was not in favor of it either and said the compromise did not go far enough.
"This represents a departure from a time honored practice in U.S. traditions and it is an intrusion of government in religious matters and private conscience," he said after attending a morning mass in Boston.
"There are other ways to achieve the goals of the administration without forcing people to go against their conscience," he said.