Immigrant rights activists vowed Wednesday to resist President-elect Donald Trump, labeled the federal immigration system racist and called on localities across the nation to adopt “sanctuary” policies and refuse to cooperate with agents trying to deport illegal immigrants.

Some groups said they’ll make the best use of the next two months to try to shield as many illegal immigrants as possible, but said real “terror” is spreading throughout their communities over the looming change from President Obama’s lenient policies to Mr. Trump’s promise of a crackdown.

Perhaps more than any other community, Hispanic and immigrant leaders took Mr. Trump’s victory hard, saying they were singled out as targets in the Republican’s “racist” campaign rhetoric.

Now, rather than advancing their agenda under the banner of Hillary Clinton, they’re preparing for a bruising struggle just to defend the gains they made under President Obama, who during his tenure halted deportations for most of the 12 million illegal immigrants in the U.S. and granted tentative legal status to more than 700,000 so-called Dreamers.

“Immigrants are declaring a state of urgency and resilience. Over the coming weeks our families and community members will need to tap into the incredible strength that brought us to this country and which we use to survive,” said Cristina Jimenez, co-founder of United We Dream, an advocacy group.

After vowing to turn out Hispanics in huge numbers to defeat Mr. Trump, advocates were left Wednesday morning wondering what went wrong and questioning the value of exit polling that actually showed Mr. Trump improving in terms of Hispanic voters over Mitt Romney four years ago, winning nearly 3 in 10.

Some advocates disputed the exit polls, saying dedicated surveys of Latinos found Mr. Trump winning less than 1 in 5, and saying that turnout was up in many Hispanic-dominated regions.

Still, Hispanics did not prove to be the bulwark Democratic nominee Hillary Clinton had hoped for, denting the community’s claims that it’s the most important demographic in elections.

Mr. Trump will be challenged to deliver on many of his immigration policy promises.

Asked about building Mr. Trump’s border wall, Senate Majority Leader Mitch McConnell demurred Wednesday, committing only to enhancing border security in general.

Mexico, which Mr. Trump has said will end up paying for the wall in one way or another, signaled it still has no intention of being forced to pony up.

Tripling the number of deportation agents, meanwhile, will cost money that Congress will have to find in an already tight budget.

But Mr. Trump could quickly cancel some of Mr. Obama’s lenient policies on illegal immigration and could restore programs that encourage state and local police to cooperate on immigration enforcement. He could also withhold federal grant money from sanctuary cities — a move that would likely force a number of places with existing policies to rethink, and could stop future cities from adopting new policies.

For now some localities were still talking tough, with Seattle’s mayor vowing in the wake of the election to maintain that city’s sanctuary policy, which prohibits reporting illegal immigrants to federal authorities.

Immigrant rights activists had been hoping for different news out of the election, in which Mrs. Clinton had promised not only to maintain Mr. Obama’s approach but to expand his deportation amnesty to millions more people and to grant taxpayer-funded lawyers to many of those facing deportation.

The switch from hope to fear was devastating.

“Today we face the tough reality that Donald Trump will be the next president of the United States, and millions of immigrants, Muslims, women and members of the LGBTQ community are scared of what the next four years will look like for our country and how this will affect them and their families,” said Cesar J. Blanco, head of the Latino Victory Fund.

Immigrants rights groups marched to the White House as the results came in early Wednesday morning and hosted rallies Wednesday afternoon. At one gathering at the University of Connecticut, activists chanted “Donald Trump is not my president.”

“My community is now on the list for deportation,” one speaker declared.

Activists insisted the surge of Hispanics voters this election was real, and said even if it wasn’t decisive in the presidential race, it did help boost Democrats in lower-tier races, such as the battle for Nevada’s Senate seat.

As for the presidential race, the results will likely be debated for the next four years.

National exit polling showed Mr. Trump winning about 29 percent of self-identified Latinos, which is higher than 2012 GOP nominee Mitt Romney’s 27 percent. That stunned Hispanic groups, who had predicted paltry support this year for Republicans across the ballot.

Matt Barreto, co-founder of Latino Decisions, a polling firm, said they surveyed more than 5,000 Hispanic voters this week across a dozen competitive states, and they reached completely different conclusions: Just 18 percent backed Mr. Trump.

He said the evidence isn’t just his polling. He pointed to a series of heavily Hispanic counties and voting precincts that went overwhelmingly for Mrs. Clinton in the election, and said it’s doubtful those kinds of places were accounted for in the exit polling, which could have skewed the exit poll results.

On an otherwise grim night, immigrant rights activists did gloat over one result in Arizona, where Maricopa County Sheriff Joe Arpaio was projected to lose his bid for a seventh term in office.

The sheriff had suffered a major setback weeks ago when the Justice Department, on the first day of early voting, announced it would pursue criminal contempt charges against him, saying he was thwarting a court order that he stop racially profiling Latinos in his county.

His efforts to try to enforce immigration restrictions at the local level made him a target for Hispanic rights groups, who poured money and volunteers into the race this year.

“The day has finally come: No longer will Joe Arpaio make sport of our lives, no longer will he parade our detained brothers and sisters in his horrifying tent city,” Mr. Blanco said. “No longer will Latinos fear Sheriff Joe Arpaio’s cruel and divisive tenure. Tonight Maricopa County chose to build bridges, not walls.”

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