The polling leader, Joe Biden, was thrown on the defensive in a private meeting with Hispanic lawmakers. They pressed him on his views about the actions of the Obama administration, which deported record numbers of Latino immigrants while Biden served as vice president.

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Several influential Hispanic leaders, meanwhile, sounded an unexpected alarm, warning that Democratic candidates are risking moving too far left in their quest to woo Hispanic voters.

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“I think there has to be some moderation. I disagree with the candidates’ positions about providing health care to undocumented immigrants, when you have Americans who don’t have health care,” said Domingo Garcia, president of the League of United Latin American Citizens (LULAC), which held its convention here. “I think that was a snap decision by some of those candidates that wasn’t thought through.”

Cecilia Muñoz, a White House aide to President Barack Obama and a former policy advocate at the National Council of La Raza, a Latino advocacy group now known as UnidosUS, said decriminalizing unapproved border crossings would make it harder for Democrats to combat President Trump’s populist appeal.

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“It allows him to make a claim that he is already making, which is Democrats are for an open border,” she said. “And it makes it harder to explain why that is not true.” She added that stopping family separations at the border doesn’t require making the crossings civil offenses.

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These concerns are part of the broader dissatisfaction Hispanic activists and officials are expressing about the Democratic field, signaling potential trouble for a party hoping to galvanize an increasingly powerful voting bloc that could play a decisive role in the 2020 election.

For many Latino activists, there is a feeling that the candidates have not gone far enough in sketching out specific policies to improve the lives of Hispanics, and that they haven’t dedicated enough time and resources to campaigning in Hispanic communities and addressing their concerns.

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“They aren’t doing enough. They need to do more,” said Rep. Pete Aguilar (D-Calif.), a member of the Congressional Hispanic Caucus. He assigned the grade of “incomplete” to the candidates, granting that they have time to improve.

His sentiment was shared by many activists here in Milwaukee at the four-day convention hosted by LULAC, the country’s oldest Hispanic civil rights group. The feature event was a town hall Thursday night with four of the presidential hopefuls, all of whom support less restrictive border laws.

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The complaints have raised questions about whether Democrats risk squandering an opportunity to extend their advantage among Hispanics. Latino voters have long favored Democrats over Republicans, but turnout has often lagged behind other groups. Signs that could be changing emerged in last year’s midterms.

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Trump’s anti-immigrant posture, blistering rhetoric and hard-line border policies helped spur a significant increase in Latino voter participation in the November midterm elections. In recent months, stories and images of migrant children suffering in detention centers and immigrants dying on journeys to the United States have stoked further outrage.

Those issues were the topic of many speeches, panel discussions and informal conversations here at the LULAC convention; during one speech, Garcia likened Trump to La Llorona, an ominous figure in Mexican mythology. They also came up in the town hall, which included Sens. Bernie Sanders (I-Vt.) and Elizabeth Warren (D-Mass.), as well as former housing and urban development secretary Julián Castro and former congressman Beto O’Rourke (D-Tex.).

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Immigration came up time and again as the candidates fielded questions separately. “Open borders is a right-wing talking point,” said Castro, defending his commitment to making unsanctioned border crossings civil infractions. “It makes no sense to make policy based out of fear, political fear.” Sanders pledged to develop a “humane policy at the border.”

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But many Democrats opted not to come to the convention — a contrast with other recent gatherings in early states such as Iowa and South Carolina, which have attracted far more candidates.

In recent weeks, many in the Democratic field, spurred by the poignant images from the border, have vied with each other to stake out immigrant-friendly positions.

During the first Democratic debate, Castro highlighted his position on border crossings, creating for a viral moment as he clashed with O’Rourke.

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Castro argues that imposing criminal penalties on people fleeing unbearable conditions is unacceptably harsh. Earlier Thursday, he sharply criticized Biden, who opposes decriminalization in favor of other solutions.

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Warren released an immigration plan Thursday that reiterated her support for decriminalization and advocated remaking federal immigration enforcement agencies. Sanders also backs moving to civil penalties.

On the Democratic debate’s second night, a moderator asked the candidates to raise their hands if their health-care plans would cover undocumented immigrants. All 10 hands shot up, reflecting the markedly different landscape from past election cycles. In 2009, Obama said in a speech before Congress that his health-care proposal would not cover undocumented immigrants, prompting a Republican congressman to yell, “You lie!”

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Despite the cautions from Latino leaders, the pressure from many Hispanic voters to embrace sweeping change has been apparent at campaign events across the country. Christian Ucles, an undecided voter who questioned Sanders at recent immigration event in Iowa, said he “1,000 percent” supports moving to civil fines for illegal crossings. He dismissed the worry that Democrats risk falling victim to Republican attempts to brand them as “open borders” extremists.

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“Haven’t they been saying that about us forever? Haven’t they been calling us socialists since, what, Kennedy?” said Ucles, 37, who came to the United States from Honduras as a young child. Even a moderate Democratic nominee “would be given the stamp of the hammer and sickle” by the right, he said, adding that Democrats should feel liberated to “go all-out.”

Similar feelings spurred immigrant rights advocates to take over the lobby of the Philadelphia building where Biden has his campaign headquarters on Wednesday, demanding he apologize for the Obama administration’s deportation of some 3 million undocumented immigrants. The activists also want Biden, and all the Democratic presidential candidates, to commit to issuing an executive order to end all detentions and deportations on their first day in office.

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Obama’s record came up at a meeting Biden held with members of the political arm of the Congressional Hispanic Caucus, according to two attendees who described the discussion.

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Rep. Linda T. Sánchez (D-Calif.) recalled reminding Biden that other priorities took precedence over immigration restructuring during Obama’s tenure. She said she asked Biden if he would he do more than pay lip service to the issue, and he responded that he would. Biden also distanced himself from Obama’s deportation policy, according to Sánchez and a second attendee.

A Biden campaign official, who spoke on the condition of anonymity to relay the details of a private discussion, recounted that Biden said in the meeting that “we didn’t get it exactly right at the beginning of the administration, but that we eventually did,” and that he also offered his vision for tackling immigration as president. Deportations dropped toward the end of Obama’s tenure.

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Biden did not attend the LULAC convention, but his wife, Jill Biden, spoke at the event.

“I think the lack of effort that was done under Obama will have an impact on Biden and he will be held accountable for that,” said Joe Henry, a special adviser to the LULAC president on civic engagement and elections who supports Castro.

Activists who attended the convention said they would like to see the candidates engage more actively with Hispanic communities. And some said they would like to see more specificity in plans for the economy and immigration that extend beyond general talk. Few candidates have issued detailed plans like Warren’s.

“Immigration reform — I haven’t heard anything that suggests to me that there’s going to be anything different,” said Vilma Seymour, 69, a retired language consultant from Richmond. “There needs to be more focus on the Hispanic community. It’s not just pandering.”

Sanders aides say they expect to release an immigration plan in coming weeks. His campaign is placing a big emphasis on building support from Hispanic voters, and aides say they see Latino outreach as a key to victory in the primary.

Chuck Rocha, a senior Sanders adviser, said the first office the campaign opened in Nevada was in the heart of a Hispanic community in East Las Vegas. The campaign is producing bilingual information and has plans for more targeted efforts. Latino activists, Rocha said, “will not be disappointed by our Latino outreach.”

Castro, the sole Hispanic candidate in the field, has also sought to stress outreach to Hispanic communities. And as candidates focus more on Nevada — the only one of four crucial early primary states with a significant Hispanic population — the emphasis on such issues may increase.

Some Democratic groups have already started strategizing to turn out Latino voters in the general election. Priorities USA, along with Latino Decisions, a premier Latino polling firm, conducted a soon-to-be-released study that will show that health care is the top priority for Latinos and immigration is a vitally important symbolic issue, according to Matt Barreto, co-founder of Latino Decisions.

Republicans, meanwhile, are signaling they will not cede the Hispanic vote in 2020. Vice President Pence recently launched a “Latinos for Trump” initiative. Among Hispanics, Trump’s approval rating is 29 percent, according to Gallup’s most recent polling, which is on the high end of where he’s been.

Sánchez, the California congresswoman, said Democratic candidates would be wise to bear in mind that Hispanic voters care about more than immigration, and to broaden their message accordingly.

“If folks think that by talking about the border or health care for undocumented immigrants, that that captures the attention of eligible voting blocs of Hispanic candidates, they’ve got a lot further to go,” Sánchez said.