Will Hillary Clinton be a champion for women in the 2016 election?

Two years after launching a project called Data2X, which aims to advance gender equality around the world, former Secretary of State Hillary Clinton on Monday kicked off the next phase of the project, announcing new partnerships to collect data on gender gaps. At Monday's event, Clinton explained why she's spearheading projects like this one.

"I have been championing the rights of women and girls around the world, as well as here at home, for many years," Clinton said, repeating a narrative she's used multiple times this year. "I got tired of seeing otherwise thoughtful people smile and nod when I raise these issues."

Clinton has indeed worked on issues relating to women and families for decades. Yet as a presidential candidate in the 2008 election cycle, the focus of her campaign fell more on her managerial credentials, with a promise that she was "ready to lead."

Eight years later, the circumstances are different. Clinton has more experience as a stateswoman under her belt, American women have embraced the concept of "leaning in," and women's issues -- such as ensuring equal pay for equal work, or requiring paid sick leave -- have come to the forefront of national conversations. Moreover, the very idea of what constitutes "women's issues" has broadened dramatically since Hillary Clinton first entered public life.

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"We've witnessed a rise in the awareness of these issues," Neera Tanden, president of the liberal Center for American Progress (CAP), told CBS News. CAP launched its own campaign focused on elevating policies to help women and families just last year.

"There's a lot more [discussion] about the treatment of working women, whether it's positive or negative," Tanden said, referencing a range of issues, from the discussion in Congress over sexual assault in the military to news reports on pay disparities in Hollywood.

These new discussions give Clinton a better chance than ever to cast herself as a champion for women and families. While she has yet to announce whether she'll launch another bid for the White House, Clinton has this year taken steps to further solidify her standing as a voice for women.

"When women participate in politics, the effects ripple out far and wide," Clinton said at the Democrats' Women's Leadership Forum Conference in September.

Clinton's focus on women and families is hardly new. In the 1970's, Clinton penned law articles about the rights of children. Those articles came under fire from conservatives during her husband Bill Clinton's 1992 presidential campaign. Her 1996 book "It Takes a Village" focuses on child rearing, while she famously declared in a 1995 speech in Beijing that "human rights are women's rights." When Clinton launched her 2008 presidential campaign, one of her first substantive policy proposals was universal pre-kindergarten.

Tanden, who worked for Clinton in the 1990's and during Clinton's presidential campaign, said she is "moderately perplexed" by the notion that Clinton is putting more focus now on women's issues.

While Clinton may not be, her party has fiercely embraced women's issues in the last two election cycles -- with mixed results. Female voters have favored Democratic presidential candidates over Republican candidates for decades, but in 2012, the Obama campaign aggressively sought to lock down that support. The president's re-election campaign slammed Republicans for waging a so-called "war on women."

After Mr. Obama won re-election with double-digit support from women, Democrats continued focusing on issues like raising the minimum wage and ensuring equal wages for women. Meanwhile, Democrats up for re-election this year continued to decry the so-called "war on women. For instance, Sen. Mark Udall of Colorado focused heavily on the charge that his Republican opponent Cory Gardner "led a crusade that would make birth control illegal."

The message fell flat in Colorado -- where Udall lost -- and elsewhere. Nationwide, women voters in 2014 favored Democrats by just a four-point margin, exit polling shows. That didn't come close to making up for the 16-point advantage that Republicans had with male voters.

Tanden contends that Democrats who spoke about more than just reproductive rights performed better with women voters. For instance, Sen. Kay Hagan of North Carolina narrowly lost her re-election bid, but she at least managed to win a 12-point advantage with female voters over her opponent, Thom Tillis.

"I think if you look at what happened in the Senate races, it shows women voters need to have a broader conversation about more than one issue," Tanden said. Candidates like Hagan, she said, focused more on economic issues like paid sick leave. "Economic issues are fundamentally important to a whole swath of voters, but women see those issues in a slightly different lens."

While women's economic issues may be more salient than ever, there's still skepticism from both the left and the right that Clinton is the optimal candidate to carry on the Democrats' pitch to working women.

Republican pollster Kellyanne Conway argued that Clinton has little in common with the average woman, aside from gender -- or even the above-average woman.

"She makes as much in one 20-minute speech as it takes the average American woman to earn in four-plus years," Conway said to CBS. "She has not driven a car since 1996. Usually, female candidates are attractive to female voters because the candidate seems accessible, relatable, regular. If anything, Hillary Clinton is shaping up to be the Mitt Romney of 2016."

Meanwhile, liberal groups like MoveOn.org are overlooking Clinton and instead coalescing behind a campaign encouraging Sen. Elizabeth Warren, D-Massachusetts, to launch a presidential bid.

"When you look at what how Elizabeth Warren connects with voters, not just in the Democratic primary but more broadly, she's speaking to issues that matter in particular to women," MoveOn's executive director Anna Galland told CBS News.

Galland hailed Warren's recent efforts to remove a "Wall Street giveaway" from a last-minute spending bill, arguing that women are "on the frontlines" in the fight against economic inequality. "Warren is someone who has spoken to the challenges of our moment better than anyone else," she said.