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WASHINGTON — Republicans vowed Wednesday to reverse President Barack Obama’s new policy on birth control, lambasting the requirement that religious schools and hospitals provide employees with free contraceptives as an “unambiguous attack on religious freedom in our country.”

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The White House pushed back in the face of a political firestorm, arguing that Obama was sensitive to the objections and looking for a way to allay the concerns. Democratic women lawmakers put up a united front in defending the administration.

“Women’s health care should not depend on who the boss is,” said Illinois Rep. Jan Schakowsky.

The fight over the administration mandate escalated as House Speaker John Boehner accused the administration of violating First Amendment rights and undermining some of the country’s most vital institutions, such as Catholic charities, schools and hospitals. He demanded that Obama rescind the policy or else Congress will.

“This attack by the federal government on religious freedom in our country cannot stand, and will not stand,” Boehner, a Catholic and Ohio Republican, said in a rare floor speech.

The contentious issue has roiled the presidential race and angered religious groups, especially Catholics, who say the requirement would force them to violate church teachings and long-held beliefs against contraception.

It also has pushed social issues to the forefront in an election year that has been dominated by the economy. Abortion, contraception and any of the requirements of Obama’s health care overhaul law have the potential to galvanize the Republicans’ conservative base, critical to voter turnout in the presidential and congressional races.

Clearly sensing a political opening, Republicans ramped up the criticism. Shortly after Boehner spoke, GOP senators gathered on the other side of the Capitol to hammer the administration and insist that they will push ahead with legislation to undo the requirement.

Sen. Kelly Ayotte, R-N.H., called the new rule “an unprecedented affront to religious liberty. This is not a women’s rights issue. This is a religious liberty issue.”

The issue is not contraception, said Sen. Marco Rubio, R-Fla., but “whether the government of the United States should have the power to go in and tell a faith-based organization that they have to pay for something that they teach their members shouldn’t be done. It’s that simple. And if the answer is yes, then this government can reach all kinds of other absurd results.”

The White House, facing a public and political outcry, engaged in damage control, circulating letters and statements from outside groups defending its position.

Administration officials had signaled on Tuesday that a compromise was possible and made clear Wednesday it was still looking for a way to deal with the issue.

“The president is committed, as I’ve tried to make clear, to ensuring that this policy is implemented so that all American women have access to the same level of health care coverage and doing that in a way that hopefully allays some of the concerns that have been expressed,” said White House spokesman Jay Carney, who added, “We’re focused on trying to get the policy implementation done in the right way.”

Options could include granting leeway for a church-affiliated employer not to cover birth control, provided it referred employees to an insurer who would provide the coverage.

Another idea, previously rejected by the administration, calls for broadening the definition of a religious employer that would be exempt from the mandate beyond houses of worship and institutions whose primary purpose is to spread the faith. That broader approach would track a definition currently used by the IRS, bringing in schools, hospitals and social service agencies that deal with the general public.

Republican White House hopefuls Mitt Romney and Newt Gingrich have been relentless in assailing the administration, criticizing the president at campaign stops. Romney has accused Obama of an “assault on religion” and Gingrich called the rule an “attack on the Catholic Church.”

But Romney has drawn criticism from his GOP rivals and the White House over policies when he was Massachusetts governor.

In late 2005, Romney required all Massachusetts hospitals, including Catholic ones, to provide emergency contraception to rape victims. Some Catholics say the so-called morning-after pill is a form of abortion.

Romney said he did not support the Massachusetts law, which passed despite his veto. But he also said at the time, “My personal view, in my heart of hearts, is that people who are subject to rape should have the option of having emergency contraception or emergency contraception information.”

White House spokesman Jay Carney seized on that policy at his daily briefing Wednesday.

“The former governor of Massachusetts is an odd messenger on this given that the services that would be provided to women under this rule are the same services that are provided in Massachusetts and were covered when he was governor,” Carney said.

He called it “ironic that Mitt Romney is criticizing the president” for a policy that Carney described as identical to the one in place in Massachusetts.

Boehner said that if the administration fails to reverse the policy, then Congress will act. He said that in the coming days, the House Energy and Commerce Committee will move ahead on legislation.

A group of House Democratic women sought to frame the issue in economic and health terms, arguing that birth control reduces health costs and stops unintended pregnancies.

In a conference call, Rep. Lois Capps, D-Calif., who said she spoke as a nurse, mother and grandmother, pointed out that 28 states have similar rules on coverage for birth control. Schakowsky pointed out that the rule affects nurses, secretaries and janitorial staff who may not be Catholic.

Rep. Gwen Moore, D-Wis., said the church “can’t impose its religious views on people and whether they can have health care.”