President Barack Obama will not make any more changes to the rule announced last week requiring health insurance plans to provide women with coverage for contraception, although U.S. Catholic bishops have said it violates the Church's religious principles.
Lew said no religious organization will be required to pay for or facilitate the coverage that it disagrees with since the insurance companies are the ones who will pay.
Asked what incentive insurance companies would have to provide contraception, Lew - Obama's budget director until a few weeks ago - said it would be cost effective just like other preventive healthcare coverage.
"This is actually one of those exceptions to the rule. If you look at the overall cost of providing healthcare to a woman, the cost goes up, not down, if you take contraceptives out."
Lew said the White House had not expected universal support for contraceptive coverage, but did find backing from several affected groups, including Catholic hospitals and charities.
"We didn't expect to get the support of the bishops or all Catholics," Lew said on "Fox News Sunday." He added on CBS's "Face the Nation" that the White House has "broad consensus, not universal consensus. This is an approach that's right."
The U.S. Conference of Catholic Bishops has issued a statement saying Obama's proposal involves "needless government intrusion in the internal governance of religious institutions".
The Catholic leaders urged Congress to overturn the rule and indicated they would also take up the issue in the courts.
The regulation at the center of the controversy requires religious-affiliated groups such as charities, hospitals and universities, but not churches themselves, to provide employees with coverage for birth control as other health insurance providers must do.
After an outcry from Catholic groups and Obama's Republican opponents, the president announced that religious employers would not be required to offer free birth control to workers and the onus would instead fall on insurers.
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.