The Republican fight against health care rights for women may end up hurting the party on election day, according to a new poll.

A Washington Post survey released Monday found that Democrats are perceived as caring more about issues that are important to women by 25 points, 55 percent to 30 percent.

The poll also showed that a large majority of all voters support the idea that businesses should be required to cover the “full cost” of contraception for female employees. Among all voters, 61 percent supported a mandate for birth control coverage, while 35 percent did not.

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Of those who said contraception should be included in insurance coverage at no cost, 79 percent agreed that religious institutions should not be exempted from the mandate. Overall, 3 percent more voters sided with Obama administration’s policy requiring religious institutions to include birth control in their insurance plans than those who did not.

As MSNBC’s Steve Benen noted, 53 percent of voters were women in 2008.

According to 2010 report (PDF) from the U.S. Census Bureau, there were 10 million more women registered to vote in 2008 and they turned out at a higher rate than men.

“The gender gap was pretty enormous four years ago,” Benen wrote. “Don’t be surprised if it’s even bigger in November.”

Photo: Flickr/thefuturistics