President Trump tosses paper towels into a crowd in Guaynabo, Puerto Rico, during a visit to the island on Oct. 3, after Hurricane Maria. (Evan Vucci/AP)

When President Trump said a few weeks ago that he wanted to find a way to continue protecting young “dreamers” from deportation, some Republicans touted the possibility of a “Nixon goes to China” moment that could reset the president’s deeply frayed relationship with Latino voters.

But ever since, Trump has returned to antagonizing this growing segment of the electorate — including proposing new hard-line immigration measures Sunday — deepening a rift that many in his party fear will do lasting damage to the GOP’s ability to win future elections.

Trump’s hostile rhetoric and actions toward Latinos, Republican strategists say, could not only undercut candidates in competitive 2018 races and make the White House harder to retain in 2020 but also further tarnish a GOP brand that party leaders have struggled for years to sell to skeptical Latino voters.

“A whole generation of minority voters is essentially hearing the GOP tell them, ‘We don’t like you,’ ” said Doug Heye, a former communications director for the Republican National Committee. “That might not have sunk the GOP against a flawed candidate like Hillary Clinton, but the demographics are moving into a direction where this will be political suicide.”

Trump’s actions have already hurt Republicans’ ability to recruit Latino candidates to run for local and state offices. And they’ve become fodder in the Virginia governor’s race, as well as contests in states such as New Mexico, Nevada, Colorado and Florida, where an energized Latino turnout could tip what are expected to be competitive elections next year.

The Trump administration released a list of hard-line immigration principles Oct. 8, which could threaten to derail a deal in Congress to protect "dreamers" from deportation. (Elyse Samuels/The Washington Post)

The latest source of tension is the president’s announcement last month that he plans to phase out the Deferred Action for Childhood Arrivals (DACA) program, a popular Obama-era initiative that provides work permits to undocumented immigrants who arrived here as children; Trump calls it “unconstitutional.”

Trump said he would work with Congress to find a way to protect the 690,000 “dreamers” enrolled in the program. But on Sunday, the White House said that what he wants in return includes the funding of a wall along the U.S.-Mexico border, a crackdown on the influx of Central American minors and curbs on federal grants to “sanctuary cities,” all policies seen as hostile by Latinos.

And Trump continues to face criticism of his administration’s response to the severe damage Hurricane Maria did in Puerto Rico.

In just the past few days, Trump has offered a cringe-worthy pronunciation of “Puerto Rico” while speaking at a Hispanic Heritage Month event, appeared insensitive by tossing rolls of paper towels at victims of Hurricane Maria and persisted in a feud with the mayor of San Juan, who has begged for more assistance in the wake of the storm.

In Virginia, which will elect a new governor next month, Trump waded into the campaign by endorsing GOP candidate Ed Gillespie in a tweet — which also charged that Democrat Ralph Northam supports the MS-13 street gang — all while Gillespie is airing TV ads that seek to tie Northam, Virginia’s lieutenant governor, to the violent gang, whose membership is mostly Latino.

Claims in the ad have been labeled misleading by nonpartisan fact-checkers and racist by immigration advocates. At issue is a tiebreaking vote Northam cast in the state Senate against a bill that would have banned sanctuary cities. But Virginia does not have any such municipalities, a fact Gillespie has acknowledged.

The president — whose job-approval rating has dipped to 16 percent among Hispanics, according to Gallup — also became a central issue in a special Florida state Senate race last month in a heavily Latino Miami-area district that flipped from red to blue. The losing candidate had appeared on Trump’s reality show “The Apprentice.”

Protesters show their support for the Deferred Action for Childhood Arrivals program at a demonstration near Trump Tower in New York. (Jewel Samad/AFP/Getty Images)

The unsuccessful GOP contender, state Rep. Jose Felix Diaz, had also joined a White House advisory board of Latino leaders and touted his close ties to Trump, even posting a selfie of the two. But when Democrats made an issue of it, Diaz deleted the photo.

Meanwhile, an ad paid for by a Florida Democratic campaign committee began with candidate Annette Taddeo turning off a television on her kitchen counter that was showing images of Trump.

“Families are too busy to worry about this drama,” she said before accusing Diaz of supporting “Trump’s every move,” including plans to cut Medicare funding and revamp the Affordable Care Act.

In North Carolina, a presidential battleground state where the Latino population is exploding, there’s been an uptick in registration by voters identifying themselves as Hispanic in the months since Trump took office — an encouraging sign, Democratic consultants there say.

Trump boosters say concerns about his standing with Latino voters are overstated, arguing that if the president continues to preside over a strong economy and create jobs, Republicans will be rewarded by voters across the board, including Latinos.

But Trump, who kicked off his campaign by calling Mexicans “rapists,” has provided plenty of reasons for Latino voters to be suspicious, including his pardon in August of Arizona sheriff Joe Arpaio, who was held in contempt of court for racial profiling.

Gallup polling suggests that there has yet to be a permanent realignment of party loyalties under Trump. As of last month, half of Hispanic adults identified themselves as Democrats or leaning Democratic, about twice as many as identified with Republicans. That is virtually unchanged since 2008.

Many GOP leaders have long argued that the status quo isn’t good enough. After Mitt Romney’s loss in the 2012 presidential race, the RNC commissioned an “autopsy” report that explored the party’s lackluster support among Latinos and emphasized a need to reach out to those voters.

“I think one can safely say that Donald Trump has not taken the 2012 autopsy report to heart,” said Whit Ayres, a longtime Republican pollster. “To this point, there hasn’t been much by the way of initiatives or language or tone that would attract anyone who’s not already in his corner.”

An American National Election Studies poll showed Trump winning 23 percent of the Latino electorate last year. Some Democratic-leaning pollsters argue that overstates his support.

Across the country, Republican consultants said they know of many cases of Latinos taking a pass on running for office because they did not want to be tied to Trump.

Juan Hernandez, who has advised Texas GOP candidates for decades, recalled trying to persuade a well-known Latino in Texas to run for Congress, but the potential contender took a pass, telling him, “I’m a Christian, I’m a Latino, and I’m a Republican, but I can’t be associated with Trump.”

“I get calls all the time from Latinos like that — all the time,” Hernandez said, confessing that he doesn’t have a good answer. “It’s very, very, very difficult.”

Leslie Sanchez, a Washington-based Latino GOP operative, agreed that recruiting candidates and cultivating younger Hispanics should be top-of-mind concerns.

“You have Gen Y, Gen Z, kind of young students in their high school or formative years in college who already believe that the president doesn’t like them,” she said. “And it’s taken an entire generation to reverse some of the falsehoods that the Republican brand had in some minority communities, and this devastates that.”

Mike Madrid, a Latino GOP consultant based in California, said part of the problem is that “DACA is a hugely important issue, especially with the emotion and energy, unlike some of the others where you can roll your eyes and say it’s Trump being Trump.”

“Will Trump ever get majority support of Latinos? No, it’s too late,” Madrid said. “But can he shore it up a little bit? Yes, absolutely.”

Sanchez said that based on polling and focus groups, she believes Latino support for Republicans has to be gauged state by state.

While the GOP is slipping in the western states of Arizona, Nevada and Colorado, the party is still performing well in states such as Florida, which is larger and more urban, with Latinos who hail from Cuba, Venezuela and Puerto Rico — where illegal immigration is not as relevant or as immediate.

Meanwhile, among Spanish-speaking Latinos, there is a “visceral” response to the GOP brand, Sanchez said.

“Republicans are going to have an extraordinarily difficult time separating the Republican brand from Donald Trump among young Latinos,” she warned.

In states with sizable Hispanic populations, Democratic gubernatorial candidates have already tried to highlight the uncertainty surrounding DACA.

In Florida, one of 36 states with governor’s races next year, Democratic candidate Gwen Graham seized on Trump’s initial announcement, calling it “utterly devoid of humanity.” In a statement, she also targeted her potential GOP opponents on the issue, accusing one of “leaving 50,000 Floridians in limbo.”

Jennifer Duffy, a senior editor at the nonpartisan Cook Political Report, said she expects Democrats to continue to make links between their GOP opponents and Trump. “It’s not just on immigration,” she said. “There’s a whole list of things. Hurricane Maria didn’t help.”

An Associated Press poll found that Trump received particularly low marks from Hispanics for his handling of the storm response. Roughly 1 in 3 Americans overall approved of the response, while about 1 in 5 Hispanics did.

Rick Wilson, a Florida-based GOP strategist, said one problem with Trump’s response is that it gives Latino voters something vivid to remember, much as George W. Bush’s detached response to Hurricane Katrina was damaging. Among other things, Trump said in a tweet that Puerto Ricans wanted “everything to be done for them.”

“There’s an anecdotal power with Katrina or Maria,” Wilson said. “People find something to latch onto. ‘Bush left us to die.’ ‘Trump said we’re lazy.’ ”