* Top Republican demands lifting of birth control rule
* White House seeks to ease objections, defuse controversy
* Republicans see Obama vulnerability on issue (Adds Democratic retreat, Carney on report of internal dissent)
WASHINGTON, Feb 8 (Reuters) - The top Republican in the U.S. Congress on Wednesday denounced President Barack Obama's new rule on contraceptives as an assault on "religious freedom" and vowed to overturn it, as the White House sought to prevent the issue from becoming an election-year liability.
Fanning a political firestorm, House of Representatives Speaker John Boehner joined an outcry from religious leaders and social conservatives over a requirement that health insurance plans, including those at Catholic hospitals, charities and universities, offer birth control to women.
Seeking to ease a controversy that has roiled the 2012 presidential race, White House spokesman Jay Carney appeared to leave the door open to compromise. He said Obama was sensitive to religious beliefs on contraception and hoped to find a way to implement the rule that can "allay some of the concerns."
But Obama, at a meeting with Senate Democrats, reaffirmed his decision and was "not equivocating," Senator Frank Lautenberg, who attended the closed-door session, told Reuters.
Republicans have seized upon the issue, seeing a chance to paint Obama as anti-religion and put him on the defensive at a time when signs of economic improvement appear to have energized his re-election bid.
The White House, caught off-guard by the fury of the response and now trying to calm objections, accused the Republicans of trying to make "political hay" out of the issue. It said it had begun outside discussions but gave no immediate sign of what, if any, concessions it might make.
"This attack ... on religious freedom in our country cannot stand and will not stand," Boehner vowed in a speech on the floor of his chamber.
The escalating fight centers on a provision in the 2010 healthcare law that requires health insurance to cover basic birth control services for women - even at Catholic charities, hospitals and universities.
Catholic bishops contend the policy infringes on religious liberty because the church does not condone the use of birth control pills or other contraceptives.
Boehner said if the president refuses to rescind the measure, Congress will do so legislatively.
But such a bill would have little chance of getting through a divided Congress. While Boehner may secure backing in the Republican-dominated House, he faces problems in the Senate, which is controlled by Obama's fellow Democrats.
No matter how Congress responds, Obama is in a political bind. A retreat would anger his liberal base, while refusal to budge could alienate some Catholic voters.
SEEKING TO CALM CONCERNS
At the White House, Carney said the administration was "focused on implementation of this rule," but made clear that it had time to try to address opponents' objections.
"There are ways to approach this that would ensure that the rule is implemented so that women have access to these important healthcare services no matter where they work, but also hopefully would allay some of the concerns," Carney said.
Carney pushed back against a New York Times report that Vice President Joe Biden and several other senior Catholic men in the administration cautioned about the political risks and were pitted against women advisers like health secretary Kathleen Sebelius, who argued in favor of the rule.
"I'm not going to get into internal deliberations," Carney told reporters. "Broadly speaking, the reports that line certain people up in some ways on this issue were inaccurate."
The rule has drawn heavy fire from the political right, including Republican presidential candidate Mitt Romney.
Carney took a swipe at Romney on Wednesday, calling him an "odd messenger" to be attacking Obama on the issue. He said it was "ironic" because Romney was criticizing Obama for pursuing a policy that is "virtually identical with the one that was in place when he was governor of Massachusetts."
Romney, speaking to reporters in Atlanta, shot back that Carney "needs to check his history," saying the birth-control provision was already in effect when he took office and that he tried to get it removed.
With the matter threatening to explode into a major election-year fight, Senate Majority Leader Harry Reid has said he and fellow Senate Democrats support the president.
"Some have decided, again, to use women's health for political football," said U.S. Representative Lois Capps, a Democrat.
Backers of Obama's new rule say employees of faith-based groups should have access to birth control services in their health insurance coverage.
The Obama administration said on Tuesday it was willing to work with church-affiliated employers to implement the new policy, which was finalized on Jan. 20 but will not take effect until next year.
During the weekend, clergy from the Catholic Church called for congregations across the country to pressure Obama to back down.
Boehner said, "Americans of every faith and political persuasion have mobilized in objection" to the rule, which he said "constitutes an unambiguous attack on religious freedom."
"This rule would require faith-based employers ... to provide services they consider immoral," he said, including, "sterilization, abortion-inducing drugs and devices, and contraception." (Additional reporting by David Lawder, Donna Smith and Richard Cowan; editing by Marilyn W. Thompson and Mohammad Zargham)