WASHINGTON, Sept. 8, 2008  -- With 57 days left until Election Day, the campaigns of both Sens. Barack Obama and John McCain are sprinting through key battleground states this week, vying for women voters who widely supported Sen. Hillary Clinton during the Democratic primaries.

Clinton -- who won 54 percent of women voters in the primaries -- campaigned for Obama today in Florida, a key battleground state.

The Obama campaign plans to send Democratic women governors and senators, such as Kansas Gov. Kathleen Sebelius and Missouri Sen. Claire McCaskill, to other battleground states.

Obama held a campaign rally on the economy in Flint, Mich., while Democratic vice presidential candidate Sen. Joe Biden toured Wisconsin and Iowa.

McCain and his vice presidential nominee, Alaska Gov. Sarah Palin, campaigned today in suburban Kansas City, Mo., where 5,000 people showed up at a campaign rally to see the running mates -- 3,000 more than could fit inside the hall where the event was held.

McCain is keeping Palin with him on the campaign trail for the first part of this week, clearly enjoying the larger-than-usual crowds energized by Palin's conservative credentials and fiery speech at the Republican convention last week.

With Palin's pick, the McCain campaign is hoping to peel away independents and women voters who identify with her "hockey mom" appeal.

Both the Obama and McCain campaigns argue they have been targeting women voters since the beginning.

However, the McCain campaign says Palin's pick has given a "shot in the arm" to their effort to recruit women volunteers -- doubling their "Women for McCain" grassroots volunteer lists since her acceptance speech.

"She's a daring and exciting pick that has really rejuvenated support and respect for Sen. McCain," McCain spokeswoman Crystal Benton said. "When she said she'd 'stand up to the ol' boys network in Washington,' that really inspired a lot of women."

Now, the McCain campaign will begin holding "Mondays for McCain," when women surrogates and women volunteers in battleground states call women voters, urging them to support McCain.

Who Will Women Vote For?

"As NFL season picks up and their husbands are watching "Monday Night Football," we thought it would be a good time to reach out to women," Benton said.

The Obama campaign argued they haven't stepped up their women's outreach efforts in light of Palin's appearance on the GOP ticket.

"Women have been a big focus since the beginning of the campaign. We're very fortunate that leaders like Hillary Clinton are out on the trail for Sen. Obama on a daily basis. They're going to continue to lay out the basic choice in this race, and remind voters that, on the issues women care about, John McCain isn't standing with them ... he's standing with George Bush," Obama spokeswoman Moira Mack said.

Obama's wife Michelle has held numerous roundtable discussions with military wives, and hosts a roundtable discussion with working women in Indiana Wednesday focusing on the economy.

"Mrs. Obama will meet with women in Fishers, Indiana to hear about their stories juggling their work and family responsibilities amidst a struggling economy. At this event, she will share with them the Obama-Biden plans to strengthen working women and their families, and prosper in a challenging economy," reads a press release sent to reporters Monday by the Obama campaign.

Obama's campaign argues efforts by McCain's campaign to target women will fall flat, given that McCain and Palin both oppose abortion rights, McCain supported President Bush's veto of SCHIP legislation that would have expanded health insurance for low-income children, and he opposed legislation that would have made it easier for women to sue in cases of wage discrimination. Palin opposes abortion, even in cases of rape or incest.

"Women voters don't trust McCain because of his extreme positions on the key issues they care about," Dana Singiser, a Clinton adviser, who is now Obama's senior advisor for the women's vote, wrote in August in an Obama campaign memo obtained by ABC News that argues "McCain cannot close the gender gap."

"Women want change from the last eight years of neglect for America's middle class families and women's economic security ... Sen. Barack Obama offers clear support for the challenges facing women and families. As president, he will expand opportunities for working women raising families and help make life affordable for stay-at-home moms. He will stand up for a woman's right to choose and for affordable birth control. He will prioritize economic security for all women by ensuring that women receive equal pay for equal work and protecting Social Security," Singiser wrote.

Do Women Identify Better with Palin or Clinton?

Before Palin joined the ticket, Obama enjoyed a lead over McCain among women, 55 percent to 37 percent, according to a recent ABC News/Washington Post poll.

However a new ABC News/Washington Post poll out today finds white women have moved from 50-42 percent in Obama's favor before the conventions to 53-41 percent for McCain now, a 20-point shift in the margin that's one of the single biggest post-convention changes in voter preferences.

Sixty-seven percent view her favorably and 58 percent say her selection makes them more confident in McCain's decision-making. Among those with children, Palin does better yet. And enthusiasm for McCain among his female supporters has soared.

The day Palin delivered her speech at the Republican convention last week, Obama was in Toledo, Ohio, where he hosted an economic town hall meeting with women, arguing he is the candidate who will stand up for women's rights.

"She's opposed, like John McCain is, to equal pay for equal work. That doesn't make much sense to me," Obama said of Palin.

The campaign also released a radio ad highlighting McCain's opposition to abortion and suggesting that he will try to overturn Roe vs. Wade.

"John McCain's out of touch with women today," the Obama ad narrator says. "McCain wants to take away our right to choose. That's what women need to understand. That's how high the stakes are."

Some Obama supporters are reportedly grumbling they would like to see Clinton use her leverage with women supporters to do more campaigning against Palin.

However Clinton remained respectful toward Palin in her comments today in Kissimmee, Fla.

"It is a great accomplishment," Clinton said of Palin's selection as the GOP's first female running mate to a crowd of 500 people. However she said the issues, not the candidates, will decide the election.

"Women as well as men make their decisions after they weigh the evidence," Clinton said. "As Americans go into that voting booth, what they have to ask themselves is not so much who am I for, as who is for me? And I don't think it's an even close question that we have the ticket that is going to do the best job in restoring the American promise."

Women Swing Vote

Former Clinton communications director Howard Wolfson, who remains an informal adviser to the senator, writes in his debut blog in The New Republic there will be "no 'cat fights'" between the senator and the Alaska governor.

"I have been asked repeatedly over the last several days to respond to the idea that Hillary Clinton will soon be dispatched by the Obama campaign to 'take Palin on,'" Wolfson writes. "The questions are fair, but what undergirds them is an obsession in our popular culture with the 'cat fight,' an offensive term that describes the spectacle of two well-known women fighting with one another.

"Don't hold your breath. It's not going to happen," Wolfson writes. "Clinton-Palin might drive ratings and sell magazines, but it wouldn't be good for the Democratic party, or the cause of women's rights. Some might enjoy the spectacle, but don't expect Hillary Clinton to play along. Hillary Clinton has spent a lifetime resisting quick and easy stereotypes, and she's not about to stop now."