Calls from progressive activists and some candidates are growing for abolishing Immigration and Customs Enforcement, created in 2003 in the aftermath of 9/11. (Sarah L. Voisin/The Washington Post)

Toward the end of his speech to Nevada Republicans on Saturday, President Trump issued a warning: Democrats were working to abolish Immigration and Customs and Enforcement, or ICE.

“They want to get rid of ICE!” the president said. “Our ICE people are so tough. They’re so much tougher than the MS-13 people.”

On Sunday morning, CNN’s Jake Tapper put the question to Sen. Bernie Sanders (I-Vt.): Did the senator, a democratic socialist and 2016 presidential candidate, the most prominent left-wing politician in the country, want to abolish ICE?

“I think what we need is to create policies which deal with immigration in a rational way,” Sanders said, evading the topic of ICE itself.

The stories of undocumented immigrant families being separated have unified Democrats, with dozens of party leaders and candidates fanning out to attack the Trump administration’s border policy. But the abolition of ICE, which has become a defining issue in some Democratic primaries, has not broken through to the party’s leading figures.

The argument, carried out online and in campaign forums, is about how to win a larger debate about immigration. Although Democratic leaders are confident in attacking Trump administration policies, they want to focus on legislation clarifying and curtailing immigration enforcement — and believe that voters want the same.

“Look, ICE is bad, but what allows abuses of ICE is a lack of reform in our immigration system,” Rep. Luis V. Gutiérrez (D-Ill.) said in a recent interview. “I don’t have to fear ICE if I’m documented.”

Supporters of “abolish ICE,” which grew quickly from a hashtag to the chant that followed Homeland Security Secretary Kirstjen Nielsen out of a D.C. restaurant this past week, want more. They argue that questioning the legitimacy of ICE, which was created 15 years ago as part of a post-9/11 government reorganization, gives the left a stronger position in any immigration negotiation.

Ideally, they want ICE to be shut down, just as some conservative activists want to shut down the Internal Revenue Service. Failing that, they want a debate on immigration that questions everything that’s being done to enforce the law.

“My read is that ‘Abolish ICE’ is the demand, and defunding ICE is the mechanism to do that,” said Sean McElwee, co-founder of Data for Progress, who coined “Abolish ICE” as a hashtag in February 2017. “In the interim, the movement has largely succeeded in making detention beds and increased funding in omnibus toxic, [and] putting incumbent Democrats on blast.”

For critics, the case against ICE is simple. For most of American history, there was no federal agency tasked with enforcing immigration law within the United States. From 1933 to 2003, enforcement was one task of the office of Immigration and Naturalization Service, but the INS was more focused on controlling immigration at official points of entry.

In 2003, the INS was shuttered and replaced by ICE, part of the new Department of Homeland Security. It was not a flash point for controversy. Then came two major changes to American life: the Trump administration, and the ubiquity of cellphone video cameras.

Starting early in 2017, immigration activists were hearing and seeing stories of ICE rounding up undocumented immigrants at schools, where they had stopped to pick up their children, and of agents setting up checkpoints, many miles from any international border, to find undocumented immigrants. Anecdote piled upon anecdote, with activists and Democratic lawmakers hearing them all.

“I saw the change in ICE almost immediately when the new president came in,” said Rep. Joseph Crowley (D-N.Y.), the fourth-ranking House Democrat. “I’d had a working relationship with them prior to that. But I sensed a new attitude here, with the director in New York, right away. It was more confrontational. They’re acting like freelance cowboys right now.”

Crowley, who does not support the abolition of ICE, has otherwise made some of the same arguments as its critics. Although the president has characterized opposition to ICE as support for the violent gang MS-13, Democrats note that he does the same for every major immigration issue, from supporting “sanctuary” status for cities to opposition to a wall along the U.S.-Mexico border. Opponents of ICE have tried to distinguish between enforcing the law against violent criminals and using the agency to round up undocumented immigrants who have otherwise obeyed the law.

Immigrant rights groups, focused on issues that seemed to be achievable in a Republican-controlled Congress, were not first to call for the abolition of ICE. That demand bubbled up from other ideological organizations, like Indivisible, the group founded after the 2016 election to organize liberals in congressional districts.

The first candidates to call for an end to ICE emerged this spring. Dan Canon, a Democrat running in Indiana’s 9th Congressional District, told McElwee in a March interview for the Nation that “ICE as it presently exists is an agency devoted almost solely to cruelly and wantonly breaking up families.” Justice Democrats, a group founded to organize and fund insurgent candidates, endorsed both the “abolish ICE” campaign and the candidates who embraced it, which in April included Randy Bryce, a labor organizer running to replace House Speaker Paul D. Ryan (R-Wis.).

On June 12, the “abolish ICE” campaign scored its first real victory when Debra Haaland, one of two anti-ICE candidates in New Mexico’s 1st Congressional District, won the Democratic primary. Last week, New York gubernatorial candidate Cynthia Nixon called ICE a “terrorist organization” and joined the call for abolition.

On June 26, the campaign will be put to a high-profile electoral test when Crowley faces Alexandria Ocasio-Cortez in the primary for New York’s 14th Congressional District. Ocasio-Cortez, making her first run for office, had made “abolish ICE” a centerpiece of her campaign, with bilingual “Abolish ICE/Elimina Ice” posters appearing in shop windows across Queens and the Bronx.

In two debates with Crowley, the longtime Democratic congressman has never defended ICE. On the trail, he has accused ICE of “fascist” behavior; in a debate broadcast last week on NY1, Ocasio-Cortez said that he had not followed that logic to its conclusion.

“If this organization is as fascist as you’ve called it, then why don’t you adopt the stance to eliminate it?” she asked. “This is a moral problem, and your problem is to apply more paperwork to it.”

Crowley responded by citing the widespread Democratic skepticism about abolishing ICE, noting that Sen. Kamala D. Harris (D-Calif.) had come out against it.

“She knows, as I do, that simply abolishing the agency does not take it out of the hands of Jeff Sessions in Washington,” Crowley said. “It’s about taking back control in Washington. It’s about Democrats taking back the House of Representatives.”

Crowley, however, inaccurately claimed that Harris had rejected the “abolish” campaign last week. She had done so in March, in an MSNBC interview that recirculated this week. On Sunday, in an interview that aired on MSNBC’s “Kasie DC,” Harris told Kasie Hunt that it was time to consider whether ICE could exist in its current form.

“We’ve got to critically reexamine ICE and its role and the way that it is being administered, and what it is doing,” Harris said. “And we need to probably think about starting from scratch because there’s a lot that’s wrong with how it’s conducting itself.”

And over the weekend, two Democrats in reliably blue districts signed on to the cause of abolishing ICE. Rep. Pramila Jayapal (R-Wash.), who represents much of Seattle, said so in an interview with the left-wing radio show “Democracy Now,” while Rep. Earl Blumenauer (D-Ore.), who represents the city of Portland, did so with a post on Medium.

Crowley’s 14th Congressional District, where less than 20 percent of voters backed Trump’s 2016 campaign, is the first where anti-ICE campaigners are targeting a Democratic incumbent. No Democratic member of Congress has lost a primary since 2014, when Rep. Seth Moulton (D-Mass.) ousted scandal-plagued Democrat John Tierney.