WASHINGTON -- President Barack Obama and Mitt Romney are engaged in a furious duel for women’s votes, battling daily with attack ads, massive rallies and heartfelt testimonials from supportive women.

In the latest round Friday, the president fired up a raucous crowd at George Mason University in Fairfax, Va., with a vigorous pitch to women voters. He wore a pink bracelet, signaling his support for breast cancer research, and was introduced by Cecile Richards, president of Planned Parenthood Federation of America.

Obama poured it on. "When it comes to issues critical to women, the right to make your own decision about your health, the right to be treated fairly and equally in the workplace, Gov. Romney wants to take us to policies more suited to the 1950s," Obama said, as the audience kept interrupting him with applause.

"He may not have noticed, we’re in the 21st century, and in the 21st century, a woman deserves equal pay for equal work,” he said. “This should be a no-brainer."

Obama went on to talk about administration efforts to make contraception and mammograms easier to obtain. The Romney campaign quickly responded by trying to shift the focus back to the economy.

“Women haven’t forgotten how we’ve suffered over the last four years in the Obama economy with higher taxes, higher unemployment and record levels of poverty," said Virginia state lawmaker Barbara Comstock.

Romney’s also trying to show a gentler, softer side, notably in a new ad this week. It features a woman suggesting Romney’s position on abortion is not as extreme as opponents say it is.

"I looked into it," the woman says. "Turns out Romney doesn’t oppose contraception at all. In fact, he does think abortion should be an option in cases of rape, incest or to save a mother’s life."

She then pivots to the economic argument. "This issue’s important to me," the woman says of abortion, "but I’m more concerned about the debt our children will be left with. I voted for President Obama last time. We just can’t afford four more years."

The Obama campaign struck back quickly with an ad featuring the woman’s picture. "Seen this from Mitt Romney?" it asked. "Then take a look at this."

“If Roe v. Wade was overturned, Congress passed a federal ban on all abortions, and it came to your desk – would you sign it? Yes or no?” asks CNN’s Anderson Cooper in a 2007 Republican candidate debate.

“Let me say it: I’d be delighted to sign that bill,” Romney says as he smiles and vigorously shakes his head affirmatively. The ad edits out the next lines that Romney said at the time. “But that’s not where we are,” he added. “That’s not where America is today. Where America is ready to overturn Roe v. Wade and return to the states that authority. But if the Congress got there, we had that kind of consensus in that country, terrific."

Romney sees a historic chance to close the "gender gap" that’s dogged Republican presidential candidates for decades. Polls suggest Romney has an opening, and he’s trying to cast himself as a reasonable, moderate leader able to fix a sluggish economy that’s hit women particularly hard.

Democrats counter by reminding women that Obama has aggressively championed abortion rights, domestic violence laws and equal pay, while Romney and his allies have been reluctant to embrace those causes .