– The politics of gender roared back into the campaign this week as Donald Trump accused Hillary Clinton of playing "the woman's card" to win votes, while his rival Ted Cruz played one of his own by announcing former Hewlett-Packard CEO Carly Fiorina as his running mate even though he's nowhere near securing the nomination.

Women are front and center in a presidential campaign that, among the Republican candidates anyway, has often uncomfortably focused on who's "man enough" to be commander in chief.

"It's an amazing moment," said Lori Nishiura Mackenzie, executive director of Stanford's Clayman Institute for Gender Research. "Hillary's very running has put women into this debate, with candidates feeling they have to respond, and that's exciting."

Now, with Trump's latest jab and Fiorina's return to the campaign after dropping her own bid to be the GOP nominee, the 2016 race for the White House is revealing what some say is a gender bias that has been nasty and nuanced, subconscious and at times over-the-top. It's something that voters across the country will have to come to terms with by November.

"In some ways, Trump's unfiltered mouth is really revealing the level of bias that is often not so clearly spoken but clearly exists," said Oakland Mayor Libby Schaaf, a Clinton supporter. "Perhaps he's doing us a favor by just laying out on the table and showing how real, how ugly and how pervasive it is in today's America."

Sen. Barbara Boxer, D-Calif., also weighed in, saying Trump's claim Tuesday that "if Hillary Clinton were a man, I don't think she'd get 5 percent of the vote" left her speechless. "In California, 80 percent of the women don't like Donald Trump. But I think he's going for 100 percent with his comments," Boxer said.

By Wednesday, not only was womancard trending on Twitter, so was Clinton's response: dealmein. "If fighting for women's health care and paid family leave and equal pay is playing the 'woman card,' " Clinton said, "then deal me in."

A nationwide Gallup poll conducted in March showed Trump's image among women growing more negative, with 70 percent holding a negative view of him, up from 58 percent in January. Women make up more than half of the electorate.

"Anyone with a heartbeat and a pulse knows how hard it is for women to get to the top, so he ought to get down from Trump Tower and realize what the world is really like for women," Boxer said.

Despite polls in the late 1990s showing nearly 100 percent of Americans said they would vote for a woman president, a 2012 Stanford study found that gender bias has "gone underground." Surveying Florida voters, they found those who quickly paired words like "president and governor" with male names and words like "secretary and assistant" with female names were 12 percent more likely to vote for a male candidate over an equally qualified female candidate.

Trump supporter Sue Ormonde said she thinks Clinton plays the woman's card. "Just because she's a woman, how does that add value?" the 69-year-old real estate agent said. "How they act, what they call a woman, what their little innuendos are, I don't care. I don't care if he gargles peanut butter. Protect my grandchildren, protect our freedom, our country and our ability to make money."

Since his campaign began, Trump has uttered a litany of disparaging comments about women, including about Fiorina's appearance, saying, "Look at that face. Look at that face."

While Trump was telling his supporters at a rally in Pennsylvania how "handsome" and presidential he looks, he also asked them, "Does Hillary look presidential?" The crowd roared back, "No!"

To academics, Trump's question was more loaded than even he may have intended, tapping into the traditional notion that presidents look like men, not women. Laura Ellingson, Santa Clara University professor of gender studies, said that Trump's calling out Clinton on the "woman's card" is "ridiculous."

"He is strategically using his masculinity to uphold his very male embodiment of a presidential candidate," Ellingson said. "He could not be more stereotypical of masculinity — he's rich, he's powerful, he's mean."

During her campaign for the Republican nomination, Fiorina had first accused Clinton of using the "gender card" and tried to neutralize gender as an issue. Whether Cruz's choice of Fiorina as a running mate will help his campaign, especially among Republican women turned off by Trump, is uncertain. Cruz is hoping to gain some traction before the June 7 primary in California, where Fiorina was a lightning rod at HP.

"Trump is a hair's breadth away from the nomination," said Larry Gerston, political science professor emeritus at San Jose State University. "This decision comes so late, like so many of the anti-Trump efforts, it's likely to affect very few people."