WASHINGTON (AP) — Democratic and Republican Senators are pouring significant time and energy into pursuing female voters, a coveted prize in the Nov. 4 elections.

Wednesday's Senate vote on contraception legislation is the latest example of Democrats' win-by-losing strategy, which forces Republicans to vote on sensitive matters that might rile women this fall.

Recent votes on "pay equity" and family leave issues were similarly aimed at women, who are increasingly crucial to Democrats' election hopes, and therefore worrisome to Republicans. Any shift in women's typical turnout or Democratic tilt this fall could determine tight elections, especially for the Senate.

Republicans need to gain six Senate seats to control the chamber, and these women's issues are especially lively in the most contested states, including Colorado, North Carolina, Arkansas and Louisiana.

Both parties must cater to their ideological bases in this midterm election year, even as they woo women who don't always vote. Nearly all Republicans are opposing measures that appear likely to expand abortion access, place new requirements on employers or limit religious conservatives' rights. And Democrats overwhelmingly support abortion access, worker benefits and equal treatment of women in the workplace.

Still, Democrats approached this week's birth control debate with different tactics, depending on whether they were seeking re-election in a GOP-leaning state or in a 50-50 or Democratic-leaning state.

Democrats knew Republicans would block their bill to counter the Supreme Court's ruling involving the Hobby Lobby arts and crafts company. The court said employers may exclude birth control products from their health insurance plans if the products violate the employers' religious faith.

Many Democratic and women's groups objected. No women "should require a permission slip from their boss" for affordable contraceptives that otherwise would be covered, Sen. Patty Murray, D-Wash., said.

Two Democrats who strongly campaigned against the court ruling are seeking re-election in states that President Barack Obama carried at least once, thanks in part to strong backing from women: Kay Hagan of North Carolina and Mark Udall of Colorado.

Minutes after all but three of the Senate's 45 Republicans voted to block the Democrats' "Not My Boss' Business" bill, Udall said his party will continue to contest a ruling that says "a boss' beliefs can supersede a woman's rights to health care benefits that she has earned."

GOP leaders defended themselves in floor speeches, press releases, TV interviews, newspaper op-eds and news conferences. Sen. Kelly Ayotte, R-N.H., said Democrats were misleading women by suggesting a Hobby Lobby employee could not buy birth control products even with her own money. "No employer can interfere with a woman employee's access to contraception," Ayotte said.

Republicans promised to push legislation guaranteeing such access.

Democrats laughed at the GOP's idea of guaranteeing people something they already have. The court ruling, Hagan said, "just shifts the additional cost back to women" who have employer-subsidized insurance from companies like Hobby Lobby. And "that could affect access" to birth control for low-income women, she said.

Other Democratic senators in tough re-election races were more cautious. Sens. Mark Pryor of Arkansas and Mary Landrieu of Louisiana were among the few Democrats who did not co-sponsor their party's bill. Pryor has said he understands the "deeply held religious views" of those who brought the Hobby Lobby lawsuit, but he disagrees with the court's ruling.

Sen. Jeff Merkley, D-Ore., enthusiastically backed the bill. His GOP challenger, Monica Wehby, is treading more lightly in a state Obama won by 13 percentage points.

The court's ruling "was very limited in scope," Wehby told reporters at the time. "As long as women have access to contraception through a third party, then I think we have to respect everyone's beliefs as much as possible."

Recent elections explain the two parties' fixation on female voters.

Women have outvoted men in every federal election since 1982, reaching 54 percent of the total in 2004, and 53 percent in 2012. Female voters preferred Democrats by 11 percentage points in 2012, while men favored Republicans by 8 percentage points.

Single women greatly preferred Obama over Republican Mitt Romney, 67 percent to 31 percent. They backed Obama over John McCain in 2008 by an even bigger margin.

The voting rate among women, and especially single women, usually drops more than male voting in nonpresidential elections. So Democrats are seeking ways to inspire women to vote this fall.

They pushed a "pay equity" bill that Senate Republicans blocked in April. It would have made it easier for workers to compare salaries and require employers to explain pay disparities.

Republicans try to turn the tables by pushing their own doomed initiatives, pitched as pro-women. Female GOP senators say they want legislation to reinforce existing laws against workplace inequities. Those efforts have about as much chance of passage in the Democratic-controlled Senate as the dozens of failed Republican bids to overturn the president's health care law, which Republicans portray as harmful to women.

"Obamacare has caused countless women to lose the health care plans they had and liked," Senate Minority Leader Mitch McConnell, R-Ky., said in a Senate floor speech this week.

His Democratic opponent, Alison Lundergan Grimes, embraced her party's Hobby Lobby position, albeit in gentle, careful tones.

"I support the right of all American women to have full access to contraception, and respect the exemption of churches from providing this service," Grimes said in a statement. The Supreme Court, she said, "got it wrong" regarding corporations.