DONNA CASSATA
Associated Press

WASHINGTON (AP) — Senate Democrats suffered what looked like a difficult setback on birth control Wednesday, but they hope it pays big political dividends in November.

Republicans blocked a bill that was designed to override a Supreme Court ruling and ensure access to contraception for women who get their health insurance from companies with religious objections. The vote was 56-43 to move ahead on the legislation — dubbed the “Not My Boss’ Business Act” by proponents — four short of the 60 necessary to proceed.

But Democrats hope the issue has enough life to energize female voters in the fall, when Republicans are threatening to take control of the Senate.

GOP senators said Wednesday’s vote was simply a stunt, political messaging designed to boost vulnerable Democratic incumbents. The GOP needs to gain six seats to seize control.

“Democrats are just trying to win an election,” Sen. Lamar Alexander, R-Tenn., said bluntly.

But Senate Majority Leader Harry Reid, D-Nev., said the Republicans were the ones “out of touch with reality.” He promised that Democrats would continue to press the issue.

Women have proven crucial in electing President Barack Obama and members of his party. And Democrats desperately need a strong turnout as they defend 21 Senate seats to the GOP’s 15, many in Republican-leaning states where Obama’s abysmal approval ratings are a likely drag.

Last month, the Supreme Court ruled 5-4 that requiring closely held companies to pay for various forms of women’s contraception to which they object violates the corporations’ religious freedom. The decision marked the first time the high court had declared that businesses can hold religious views under federal law.

“Five men on the Supreme Court rolled back the clock on women in America,” said Sen. Patty Murray, D-Wash.

A Senate veteran — the four-term Murray — and an incumbent locked in a tight race — Colorado’s Mark Udall — joined forces in pushing the legislation that would have reversed the court’s decision by providing access to contraception through insurance plans at businesses that object on religious grounds.

Republicans asserted that the government must accommodate the deeply held religious beliefs of Americans, including the owners of Hobby Lobby, the Oklahoma-based chain of arts and craft stores that challenged the contraceptives provision in the law.

“The issue in Hobby Lobby is not whether women can purchase birth control, it’s who pays for what,” said Sen. Deb Fischer, R-Neb., in remarks on the Senate floor. “Those of us who believe that life begins at conception have moral objections to devices or procedures that destroy fertilized embryos.”

Fischer said the Green family, which owns Hobby Lobby, has similar objections and “they don’t want to use their money to violate their religious beliefs.” She said the company’s health coverage does pay for 16 of 20 forms of contraception, including birth control pills.

Senate Minority Leader Mitch McConnell, R-Ky., said Democrats “think they can score political points and create divisions where there aren’t any by distorting the facts.”

McConnell joined with two Republican women, Fischer and Sen. Kelly Ayotte of New Hampshire, in backing separate legislation that would reaffirm current law on access to contraception and in calling for a Food and Drug Administration study on whether contraceptives could be sold over the counter without a prescription.

In one of the most closely watched races in the country, McConnell faces Democrat Alison Lundergan Grimes in his bid for a sixth term.

On Wednesday’s vote, three Republicans broke ranks with their party — Susan Collins of Maine, Lisa Murkowski of Alaska and Mark Kirk of Illinois — and backed the Democratic-led legislation. In a procedural move, Reid switched his vote to no, allowing him to bring the measure up for another vote closer to the election.

All other Democrats backed the bill.

Democrats facing re-election insisted that the court ruling would force some women to pay out of pocket for contraceptives, or simply skip the purchase if the cost was too much.

“When you charge women more for contraceptive coverage, then you are denying them access to that care,” said Sen. Jeanne Shaheen, D-N.H., who is in a competitive race.

The government has said nearly 30 million women receive birth control as a result of the four-year-old health care law.

In the 2012 presidential and House elections, Democrats captured the female vote by double-digit margins — 55 percent to 44 percent — as Obama won re-election, according to exit polls conducted by Edison Research for The Associated Press and other news organizations.

Democrats enjoyed a slightly better edge in the 2008 elections when Obama captured his first term and Democrats maintained their congressional majority.

But it was far different in the 2010 midterm elections, some eight months after Obama signed the health care law and as the tea party energized the GOP. Female voters backed Republicans 49 percent to the Democrats’ 48 percent in a low-turnout election that enabled the GOP takeover of the House.

In Colorado in 2008, female voters were critical to Udall’s election to the Senate, favoring his candidacy 56 percent to 41 percent while men backed him 50 percent to 46 percent.

Ilyse Hogue, president of NARAL Pro-Choice America, said the court’s decision has “awakened the pro-choice majority in this country.” In Kentucky, NARAL began a 30-second ad criticizing McConnell for his opposition to the legislation.

Democratic candidates in other states have been pressing their GOP rivals on whether they supported the court’s ruling.

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Associated Press Director of Polling Jennifer Agiesta contributed to this report.

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