LAREDO, Texas — Just a month after President Biden took office, pledging to roll back Trump-era policies in an attempt to take a more humane approach to immigration, Representative Henry Cuellar, a Democrat from South Texas, began to sound an alarm.

He warned that the number of migrants seeking to enter the country would rise, and soon released photos of children sleeping under tinfoil blankets at a crowded migrant processing facility in his district at the edge of the U.S.-Mexico border.

Now Mr. Cuellar, 68, has become one of the administration’s most consistent critics on immigration, appearing on Fox News and at times echoing Republicans, saying immigrants are pouring into the United States because they believe “that the border is open.”

His criticism has been met with fierce resistance from Jessica Cisneros, 28, a progressive immigration lawyer who is trying to unseat him in a Democratic runoff on Tuesday.

Like other Democratic primary contests, their race is a proxy battle for the broader direction of a party that is being tugged between moderate and progressive wings. But in particular, it encapsulates the acute tensions within the party on immigration.

In interviews with Democratic leaders and voters in Texas’ 28th Congressional District, which stretches from Laredo to San Antonio, many expressed a deep frustration with both national Democrats and Republicans who use the border as a political backdrop but have failed to overhaul the nation’s immigration laws, combat the drug trade or improve legal pathways to citizenship.

And many worried that Democrats lack a forceful and coherent message when facing Republicans who have appeared increasingly intent on portraying a migrant “invasion,” making it a marquee issue of the midterm elections.

Mr. Cuellar is often at the center of the debate. His supporters say he is simply trying to balance competing Democratic factions on the issue, as the G.O.P. has largely abandoned policy-centered debate in favor of anti-immigrant appeals. But he is criticized just as much by Democrats concerned he sounds too much like a Republican, focused on enforcement rather than a humanitarian approach.

“He is opening the door to something that can get really, really ugly, really, really quick,” said Maxine Rebeles, a middle-school teacher and immigrant activist with the No Border Wall immigrant rights coalition based in Laredo.

Outside a bustling polling station at a Laredo firehouse, where a light breeze provided respite on a sweltering day, Mr. Cuellar rejected the criticism from what he called the far left. He said he favored immigration proposals to help workers, and pathways to citizenship for people who were brought to the country illegally at a young age.

But Mr. Cuellar, whose brother is the Webb County sheriff, said he also was attuned to the needs of community leaders and immigration officials in his district who have voiced concerns about the lack of resources to process increases in arriving migrants.

“I speak against the Republicans who want a fence or a wall, I speak against them when they call this an invasion — it’s not an invasion,” Mr. Cuellar said in between bantering with supporters. But, he added, “I am in the middle — speaking against both sides.”

Mr. Cuellar, who is in the political fight of his career, remains part of an open F.B.I. investigation, though officials have not released any details.

Asked whether Democrats were lacking a cohesive message on immigration, Mr. Cuellar agreed. He said he was most worried that Republicans were filling that vacuum by painting Democrats as soft on crime.

Asked the same question, Ms. Cisneros took a shot at members of Congress out of step with the Biden administration, like Mr. Cuellar, who she said was playing into the kind of right-wing talking points that had fueled white supremacist mass shootings in Buffalo and El Paso.

“Henry Cuellar is pivoting to these xenophobic lines of attacks that just create a target on our backs,” said Ms. Cisneros, who called Mr. Cuellar “Trump’s favorite Democrat.” She added that she would bring her own professional experience as an immigration lawyer to bear when shaping border policy.

For years, conservative Democrats who represent border communities, like Mr. Cuellar, have sought to strike a balance: espousing the benefits of immigration for trade, business and the social fabric of their predominantly Latino communities, while talking tough on the need to increase funds for surveillance and law enforcement along the southern border.

But that balance has slipped out of reach. Attempts to pass bipartisan immigration laws have failed for decades, and harsh anti-immigration language and policies have become central Republican approaches since the rise of former President Donald J. Trump.

Republicans in this midterm cycle have poured nearly $70 million into 325 unique ads on border security and immigration, many painting dystopian conditions at the nation’s southern border and several using language of “invasion,” according to the ad-tracking firm AdImpact.

Democrats, by contrast, have spent only $8 million on 46 ads on immigration — and one from Mr. Cuellar attacked Ms. Cisneros for progressive immigration policies he claimed would cut border enforcement officers’ jobs and lead to “open borders.”

Democrats at first seemed to move to the left in response to the Trump administration’s harsh stance on immigration issues. During the 2020 presidential primary, most candidates backed a policy of decriminalizing border crossings. But since then, some in the party and in pro-immigrant organizations have criticized what they see as backtracking on the issue as Republicans double down.

Marisa Franco, who served on the immigration committee of a Democratic unity task force formed by President Biden and Senator Bernie Sanders of Vermont, calls the party’s stance on immigration “capitulation.”

“Republicans are putting out solutions — and instead of countering their horrible solutions, Democrats are either not talking about it or they’re by default legitimizing the point of view that immigration and immigrants are bad,” said Ms. Franco, the executive director of Mijente, a liberal Latino advocacy group. “In the face of really nasty stuff, they’re ducking and running.”

A particularly glaring example of Democratic divisions is Title 42, the pandemic-era policy enacted by the Trump administration that swiftly turns away nearly all migrants seeking asylum at the border.

The Biden administration had kept the policy in place for more than a year, but sought to lift it earlier this year as other pandemic restrictions eased. That decision set off a flurry of lawsuits and a parade of Democrats trying to distance themselves from the president. On Friday, a federal judge upheld the policy.

The criticism of the Biden administration’s attempt to overturn Title 42 has come from Democratic members of Congress facing tough re-election fights all over the country, including Mr. Cuellar and Senators Catherine Cortez Masto of Nevada, Raphael Warnock of Georgia and Maggie Hassan of New Hampshire.

And Senators Kyrsten Sinema and Mark Kelly of Arizona, both Democrats, have repeatedly criticized the Biden administration’s plan to lift the policy and introduced a bill last month to prevent it without a detailed plan to stop an expected increase of migrants at the border.

The inaction could prove costly this election year: Some organizations that helped win crucial swing states for Democrats in 2018 and 2020 have no plans to knock on doors or call voters this midterm season, because they are so furious at the party’s stance on immigration.

Among them is Lucha, an advocacy group in Arizona widely credited with helping secure wins for Ms. Sinema and Mr. Kelly, the first Democratic senators to represent the state in decades.

“For that incredible effort and incredible turnout, we’ve gotten very minimal results,” said Tomas Robles, its co-executive director. “Democrats are falling into the same trap — there’s a lack of political will and courage.”

In Laredo, a city of roughly 261,000 people where downtown shops and parks seem almost to blend into the border, the nation’s immigration fight is personal. Members of the No Border Wall coalition, which is nonpartisan, are quick to note that they have successfully repelled four attempts by Democratic and Republican administrations to build a wall in the region.

But Laredo Democrats united in their battle against the wall are split on support for Mr. Cuellar and Ms. Cisneros, and their approaches to immigration. Mr. Cuellar continues to follow the path taken by the Obama administration, which relied on an aggressive border enforcement strategy meant to entice Republican support for a path to citizenship for millions of undocumented immigrants.

His backers tend to subscribe to the same philosophy — or at least to accept it. “He’s much more conservative than I would prefer,” said Melissa R. Cigarroa, board president of the Rio Grande International Study Center. “But he doesn’t stop working for the community.”

But supporters of Ms. Cisneros argue that the emphasis on border security has not helped create legal avenues to citizenship. It also, they argue, does little to counter an “us-versus-them” approach pressed by Republicans that has put asylum seekers and migrants in danger. “Cisneros comes from that side, of helping families,” said Juan Livas, an immigration activist and co-founder of the Laredo Immigrant Alliance.

The schisms reflect the national divide among Democrats, while Republicans have remained largely united in favor of tough policies aimed at limiting immigration.

“It’s hugely disappointing and demoralizing and even enraging,” said Representative Jesús G. Garcia of Illinois, who has sponsored immigration reform bills. “We said if we win majorities in both chambers that it would produce immigration reform.”

That hasn’t happened, he said, and the party instead has assumed a defensive position. “It’s a political calculus, and I think it’s a mistake,” he said.

Azi Paybarah contributed reporting.