“This opens a door that wasn’t open to us before,” Ms. Montelongo said. It does not hurt, she added, that the abuelas are seldom wallflowers.

“They’re not afraid to be direct,” she said. “They have the harder conversations that we can’t always have with people who we want to be supporters.”

She offered a bit of advice gleaned from personal experience: “Don’t mess with them.”

Turnout among Latinas, and among minority women more broadly, is one of the more overlooked aspects of a presidential campaign that has focused so much on swaying white, college-educated women. But minority women were a critical factor in President Obama’s 2012 re-election. Black women turned out at a rate of 70 percent — higher than any other group. Latina turnout was 50 percent, exceeding Hispanic male turnout by four percentage points.

Three-quarters of women newly eligible to vote since 2000 have been minorities, according to an analysis of census data published by the Center for American Progress, and Latinas made up the biggest chunk. There are now at least 5.9 million more of them who can vote than there were when George W. Bush was first elected — an 83 percent increase. At the same time, population growth among white women has plateaued.

The trend is especially pronounced in Arizona, where the Latina voting-age population has grown by almost 70 percent since 2000. In a sign of their nascent political power and high level of engagement, Latinas here have made up a larger share of the electorate in midterm elections, when far fewer people vote on the whole, than they have in presidential years, the Center for American Progress said.

“There’s a saying that I never forget,” said Barbara Valencia, 64, a retired college administrator who lives in Tempe. “You educate a man, you educate a person. You educate a woman, you educate a family.” Ms. Valencia, like Ms. Cañez, is part of a group of Hispanic women in their 50s, 60s and 70s who are working with the state Democratic Party to bolster turnout in their communities.