(Reuters) - The Senate is expected Thursday to defeat a largely symbolic measure that would exempt employers such as Roman Catholic hospitals, universities and charities from a controversial White House rule requiring free birth control coverage.

Debate on the Republican proposal, introduced by Missouri Senator Roy Blunt as an amendment to an unrelated highway bill, began on Wednesday and both parties seized the opportunity to play to voting constituencies considered crucial in November's election.

The Obama policy requires almost all employers who provide health insurance to provide coverage for women's contraceptives without copays or deductibles. It is vehemently opposed by social conservatives and Roman Catholic bishops on moral and religious grounds.

Democrats, seeking to turn the debate into an appeal to independent women voters, have sought to cast themselves as defenders of women's healthcare, while Republicans are pushing a religious liberty argument that could resonate with Catholics and other social conservatives in important swing states.

Polls show a divided public. A recent Gallup survey found that adults agreed with religious leaders who oppose Obama's birth control policy over the Obama administration on the contraception issue by a 48 percent to 45 percent margin. The poll has a 4 percentage point margin of error.

Each party, accusing the other of politicizing the issue, has produced special-interest allies - from religious and anti-abortion groups to physicians, nurses and health-related charities.

The Republican Party suddenly wants to turn back the clock and take away contraception from women. Make no mistake: that's what this debate is about, New York Democrat Charles Schumer said in the Senate on Wednesday.

The debate today is not about access to contraception, Indiana Republican Dan Coats countered. What this debate is really about, is whether Congress is going to sit by and idly allow this administration to trample freedom of religion.

The dispute played out on the campaign trail, where Republican presidential hopeful Mitt Romney told the Ohio News Network in an interview that I'm not for the bill - before a campaign spokesperson said the former Massachusetts governor was thrown off by way the reporter had framed the question.

Regarding the Blunt bill, the way the question was asked was confusing, said Romney spokeswoman Andrea Saul.

Governor Romney supports the Blunt bill because he believes in a conscience exemption in health care for religious institutions and people of faith, she said in a statement.

LATEST FLIP-FLOP?

Obama's campaign lost no time in pointing to Romney's remarks as evidence that showed why women don't trust him for one minute.

It took little more than an hour for him to commit his latest flip-flop. Even worse, he ended up on the wrong side of an issue of critical importance to women, said Stephanie Cutter, Obama's deputy campaign manager.

Kathleen Sebelius, Secretary of Health and Human Services, issued a statement calling the amendment dangerous and wrong and saying that it would affect treatment beyond contraception.

The Obama administration believes that decisions about medical care should be made by a woman and her doctor, not a woman and her boss. We encourage the Senate to reject this cynical attempt to roll back decades of progress in women's health, she said.

The contraceptive-coverage rule was adopted according to a provision in Obama's 2010 healthcare reform law. It covers a wide range of preventive services and has been billed by administration officials as a step intended to reduce unwanted pregnancies and related health problems as well as abortions.

But the rule quickly came under attack from social conservatives led by Catholic authorities who argued it was a violation of religious freedom.

In an attempt to quell the election-year firestorm, Obama earlier this month announced that religious employers would not be required to offer free birth control to workers and the onus would instead fall on insurers.

Church leaders have dismissed the compromise as a gimmick that would still trample the church's constitutional right to oppose artificial contraception.

While Republicans have backed the Blunt amendment in the Senate, some opponents have gone to court. Seven U.S. states have joined Catholic groups and individuals in a major federal lawsuit in Nebraska.

(Additional reporting by Thomas Ferraro; Editing by Cynthia Osterman and Philip Barbara)