And with African-American turnout so far failing to match the historic levels of 2008 and 2012, Hispanics could make up the difference. In fact, they could turn out to be Mrs. Clinton’s firewall.
In Florida, a state that is likely to be decided by the thinnest of margins, about one million of the nearly 6.2 million early votes counted as of early Sunday had been cast by Hispanics, an increase of almost 75 percent over 2012. In Clark County in Nevada, home to Las Vegas and the state’s largest Hispanic population, a record 57,000 people voted on Friday alone.
Eight years ago, President Obama inspired a wave of African-American turnout, with black voters hopeful and deeply moved by his candidacy. This time, it is not an admired figure but a disliked one — Mr. Trump — who is driving the surge among Hispanics.
Motivated by fear about what a Trump presidency would mean for their families, many Hispanics say they cannot afford to stay home.
“I’m scared for my country’s future,” said Cinthia Estela, 30, who is helping to organize Latinos for the Arizona Democratic Party. Sometimes, Ms. Estela brings along her mother and two young daughters, who are 8 and 9, to help in the effort.
“This is breaking us apart,” she said of the election. “This is taking us back many years.”
Crucially, many of the Latinos casting ballots are new voters. According to an analysis of early vote returns in Florida by Daniel A. Smith of the University of Florida, more than one-third of Hispanics who have cast ballots so far did not vote in November 2012.
“It is truly historic,” Mr. Smith said. “Donald Trump has done more to energize Hispanics in Florida than any Democratic candidate.”
But the Democrats were laying the groundwork even before Mr. Trump emerged as the Republican nominee, with years of organizational planning and tens of millions of dollars in investment by pro-immigration groups, state Democratic Party organizations and the Clinton campaign itself.
From the beginning of her campaign, Mrs. Clinton and her team saw untapped potential in the 27 million Hispanics who would be eligible to vote in 2016, a 26 percent increase since 2012.
But voter turnout among Hispanics was stubbornly low. In the 2012 presidential campaign, 48 percent of eligible Hispanics voted, compared to 64 percent of eligible white voters, according to Pew.
So they set out to reach them in their communities, talking to them in their language, with the belief that touching them in the most personal way possible, at churches, bodegas, bus stops and nail salons, was also the most persuasive. And the effort was focused on more than registering potential voters. Democrats sought to make electoral politics part of the daily conversation for a demographic that had until now largely sat on the sidelines.
Starting in Nevada, the campaign convened groups of women to discuss issues that were important to them, like health care and education. After each meeting, the women were asked to write down the names and contacts of five other women who might support Mrs. Clinton. The program, called “Mujeres in Politics,” was deemed such a success that the campaign replicated it in Colorado and other states with large Hispanic populations.
“We understand this community. We know culturally what are the strongest messages that work for them,” said Lorella Praeli, Mrs. Clinton’s national director of Latino Outreach, who had lived undocumented for years after coming to this country from Peru. “This wasn’t created in an office. This was built on the ground.”
Mrs. Clinton also had to grapple with the fact that many Latino voters were disappointed with Mr. Obama, who had increased deportations and failed to bring about an overhaul of the country’s immigration laws. Mrs. Clinton knew she would need to tell Latino voters at the start of her presidential campaign that she would go further than Mr. Obama in extending a path to citizenship, even if it meant upsetting the president.
Mrs. Clinton and her Democratic allies now have a presence in every state with a large Hispanic population with customized strategies for each.
In Florida, the campaign identified early on the influx of Puerto Ricans who had fled the island amid its economic crisis as a potential bloc of new Democratic voters. Both Bill Clinton and Amanda Renteria, the campaign’s political director, were dispatched to Puerto Rico. And the campaign issued bilingual messages of support for funding to combat the spread of the Zika virus and to encourage legislation to address the debt crisis in Puerto Rico.
In Arizona, a state Democrats believe they have a chance of winning for the first time since Mr. Clinton carried it in 1996, Mrs. Clinton and her allies have focused much of their efforts on the restrictive immigration policies that have been approved by the Republican-led state government.
Ian Danley, executive director of One Arizona, a coalition of 14 organizations that lead voter mobilization efforts, said the group was sending 350,000 text reminders to Latinos, urging them to vote.
While Hispanic turnout this year is largely driven by on-the-ground voter outreach, Mrs. Clinton has also paid careful attention to select the right issues.
And there are few issues that have bonded her as closely to Latinos as immigration. On the polarizing questions surrounding what to do with undocumented immigrants, Mrs. Clinton has taken a more sympathetic posture than many in her party have, including the president, whom she has criticized as acting too aggressively on deportations.
She has embraced undocumented immigrants in a way that would have been practically unthinkable when her husband ran for president in 1992. And she has pledged to make the politically combustible issue of immigration reform a priority of her first 100 days in office if elected.
The Democrats have especially leaned on Hispanic women for their campaign. Similar to how black women became an influential engine of support for Mr. Obama, Hispanic women have been central to the organizing efforts of Democrats.
Latinas have been working phones and knocking on doors, often in mother-daughter pairs. And they say they are hearing the same story again and again from the neighbors they have persuaded to go to the polls: They have never voted before, but feel they must now because they cannot stomach the thought of Mr. Trump in the White House.
Asked if there was anything in particular that drove him to the polls in West Tampa, Fla., on Sunday, Oscar Diaz, 44, a maintenance worker with Puerto Rican roots, said simply, “Trump’s big mouth.”