CONCORD, N.H. — While the issue of birth-control coverage plays out nationally, New Hampshire’s Republican-controlled House voted today to allow employers with religious objections to exclude contraceptive coverage from their health plans.

The House voted 196-150 to send the bill to the GOP-dominated Senate after a floor debate in which Republican House Speaker William O’Brien at one point threatened to empty the House gallery when bill opponents cheered as arguments were made against the bill.

The measure’s fate in the Senate is uncertain. Gov. John Lynch, a Democrat, has not said if he would veto the bill.

“The governor has serious concerns about the bill. Our current law is working well,” Lynch spokesman Colin Manning said today.

The New Hampshire Civil Liberties Union has said it would sue to block the change, arguing that it would open the door to other kinds of discrimination.

O’Brien, who is Catholic, began championing the exemption after the federal government issued a rule requiring health insurance companies to provide contraceptives to employees of religious organizations. He accused President Barack Obama of using the issue to woo women to vote for him in November.

He and other GOP leaders last month along with Catholic Bishop Peter Libasci called for the federal requirement to be overturned even though Obama announced after an uproar over the rule that it no longer mandates religious organizations to directly pay for contraceptives.

It was not clear today how the federal requirement would affect the New Hampshire exemption if it becomes law.

O’Brien argues that people who don’t agree with the exemption can either pay for birth control out of their own pockets or choose to work for a different employer.

“New Hampshire has a long and proud history of religious tolerance,” Deputy House Speaker Pamela Tucker, a Greenland Republican, said in support of the measure.

Rep. Jennifer Coffey, R-Andover, said women who need contraceptives to address a health issue other than to avoid pregnancy would still be able to get prescriptions covered by health plans.

“This says no pills, no condoms for the sole purpose of preventing pregnancy,” she said.

Dozens of women gathered at the Statehouse to demonstrate against the bill. NARAL Pro-Choice New Hampshire also held a news conference in the Legislative Office Building across the street as the debate neared a conclusion.

“Who would have imagined that with the advances made by women in nearly every sector of society, we would be facing legislation that not only turns back the clock, but so dramatically attacks a most basic and fundamental right of women,” said the Rev. Mary Westfall, pastor at the Durham United Church of Christ.

“Who would have imagined that in a state that so values personal rights and liberties, a piece of legislation would even be seriously considered that so erodes those very rights? Who would have imagined,” she said at the news conference.

New Hampshire is one of 28 states with laws or regulations requiring equity in private insurance coverage for contraceptives, according to Laura Thibault, interim executive director of NARAL’s state organization. Eight of the 28, including New Hampshire, have no exemptions for religious organizations, she said.

The remaining states have opt outs for churches and some allow schools, universities and hospitals to refuse the coverage, according to Thibault. Besides New Hampshire, a handful of other states are considering repealing the mandatory coverage, she said.

The 12-year-old law O’Brien proposes to change only requires coverage of contraceptives if other drugs also are covered. Employers also can avoid state mandates altogether by self-insuring.

But opponents argued that the constitutional protection of religious freedom does not apply to an institution entering the marketplace to buy insurance.

“Offering a health care benefit to employees is not an expression of religious faith. It is a business decision,” said Rep. Christopher Serlin, D-Portsmouth.

Serlin said once an employer enters the marketplace “they need to abide by the same laws we do.” He said if the bill truly was to protect religious freedoms it would have included the Jehovah’s Witness religion, which forbids blood transfusions.

Last week, radio personality Rush Limbaugh apologized to Georgetown University law student Sandra Fluke for calling her a “slut” and “prostitute.” Limbaugh made the remarks after Fluke testified to congressional Democrats in support of national health care policies that would compel employers and other organizations to offer health insurance that covers birth control.

Limbaugh apologized on Saturday after advertisers began leaving his show.