Senate Democrats believe they have Republicans boxed in. They think the push for the Blunt amendment and Rush Limbaugh’s attacks on Sandra Fluke are damaging Republicans among key swing constituencies — women and independents — and that Republicans would like this whole battle to go away.

But Republicans can’t put this behind them, Dems believe, because the conservative base is still itching for this fight to continue.

Today, in an effort to exacerbate this dynamic, all dozen female Democratic Senators will call on House Republicans to drop this battle once and for all.

In a letter to Speaker John Boehner — which was sent my way by a source — the 12 female Senate Dems, led by Patty Murray, are demanding that he drop his promise to hold a vote on the House version of the Blunt amendment, which has over 200 Republicans co-sponsors.

The letter from the female Senators — which is timed to International Women’s Day — asks Boehner to pledge not to move any more birth-control-related legislation in the House.

“We are asking that you abandon the promise you have made to bring legislation to the House floor similar to the Blunt amendment, which was defeated in the Senate last week, and which would turn the clock back on women’s access to health care,” the letter says. “We ask that you listen to the overwhelming outcry from American women who support access to contraception and drop all politically-charged efforts to deny them coverage.”

The letter represents an effort to force Boehner’s hand by getting him to declare clearly whether the House will vote on its Blunt amendment, or whether he intends to let the controversy fade way quietly. Now that the Senate has voted Blunt down, even some Senate Republicans are conceding that they want this issue put behind them. The question remains whether conservatives will allow this, and whether the House will hold its own vote.

New polling sponsored by EMILY’s List and Planned Parenthood Action Fund finds that in key Senate battlegrounds, GOP support for Blunt boosts Dem candidates who support access to birth control.

Dems believe that swing voters have accepted their framing of this fight, and don’t see it as a battle over religious liberty, but as one over access to contraception, women’s health, and the GOP’s hidebound ideas about women’s rights. “For most American women, the battle over contraception was settled a half century ago,” the letter says. “Women have had enough.”

Full letter — which is signed by senators Murray, Mary Landrieu, Barbara Boxer, Claire McCaskill, Jeanne Shaheen, Maria Cantwell, Kirsten Gillibrand, Dianne Feinstein, Amy Klobuchar, Debbie Stabenow, Kay Hagan, and Barbara Mikulski — after the jump.

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Here’s the letter:

Speaker Boehner,

We write to express our concerns over your recent statements pledging to continue efforts to put employers between American women and their access to birth control. Specifically, we are asking that you abandon the promise you have made to bring legislation to the House floor similar to the Blunt amendment, which was defeated in the Senate last week, and which would turn the clock back on women’s access to health care. Furthermore, we ask that you listen to the overwhelming outcry from American women who support access to contraception and drop all politically-charged efforts to deny them coverage.

Today, at a time when 99% of sexually active women in the U.S. have used birth control, its role in the lives of women and their families is hard to understate. Access to birth control is directly linked to declines in maternal and infant mortality, can reduce the risk of ovarian cancer, and is linked to overall good health outcomes. Nationwide, 1.5 million women use contraceptives only as treatment for serious medical conditions. And most importantly, access to birth control helps reduce the number of unintended pregnancies and abortions, a goal we all share.

That is why the recent Republican attacks on birth control access have been so eye-opening for American women. For most American women, the battle over contraception was settled a half century ago. Yet, over the course of the past month alone, women have watched as panels on birth control have been convened without women, a young woman that dared to speak out in defense of birth control was subjected to vile name-calling, and extreme legislation, like the Blunt Amendment, has been pushed to deny access.

Women have had enough. As we have heard from countless women in our home states and here on Capitol Hill, they are tired of being targets for a political strategy that endangers their health care and they want it to stop. We hope that you can answer their calls, and ours. It’s time for you to put an end to the attacks on women’s health care and to work with the Senate to get back to the American people’s top priority: creating jobs and boosting our economy.