For generations, Chicago’s Brighton Park neighborhood has been made and remade by successive waves of immigrants.

So many arrived from Poland that Pope John Paul II, who was Polish, paid a visit in the 1970s. When Polish and Lithuanian families were moving out in the 1990s, Mexican Americans bought houses, opened businesses and forged a bilingual community. And in the last few years, as the city’s Asian population has boomed, Chinese Americans have joined them.

But even here, people are divided over a hastily conceived plan to convert an empty lot into a winterized tent complex for 2,000 or more migrants, many of them Venezuelan.

Chicago, New York City, Denver and other liberal cities have been overwhelmed this year by migrants sent northward from border states, a surge that has strained social services, frayed residents’ patience and put municipal pronouncements of sanctuary to the test. A look at this one neighborhood, where immigration is woven into family stories and streetscapes, shows the depth of the challenge facing cities as busloads of newcomers keep arriving.

In Brighton Park, some residents learned about the planned encampment as heavy machinery rolled onto the 10-acre site. In the days since, they have protested, posted angry social media messages and packed an informational meeting in a high school auditorium, where some applauded city officials and others heckled them.

Demonstrations at the Brighton Park site, on a busy stretch of road where industrial land begins to fade into residential, have at times grown contentious, surprising some who thought of their neighborhood as a haven for immigrants.

“I was thinking that a place like Brighton Park could be such a positive place,” said the local City Council member, Julia M. Ramirez, a progressive Democrat who was swarmed by protesters and, she said, physically assaulted when she visited the site.

Ms. Ramirez, a social worker whose family has roots in Mexico, said she did not suggest any sites for migrant shelters to the new mayor, Brandon Johnson, and that she was reserving judgment on the merits of the encampment. But she described reasons to think migrants might thrive in Brighton Park: Experienced educators can teach English as a second language, Venezuelans can conduct business in Spanish, many neighbors can empathize with being a newcomer.

About 40 percent of Brighton Park residents were born outside the United States, according to data compiled by the Chicago Metropolitan Agency for Planning, and more than 70 percent of residents speak Spanish.

“Being able to resonate with the story of leaving something and trying your hardest to start something new,” Ms. Ramirez said. “No matter your race, that is prevalent in Brighton Park.”

In interviews and public comments, others described the planned encampment as a grave threat to a neighborhood where they had sacrificed for years to gain a foothold.

Though Brighton Park has challenges — the median income is well below the city average, industrial pollution is a persistent blight and violent crime is a constant concern — it is a bustling place with walkable commercial strips, stately church buildings and verdant residential blocks where motorists are slowed by mountainous speed bumps.

Situated off the expressway about six miles southwest of the downtown Loop, it includes a mix of residential blocks, industrial sites and trucking yards. Boeings bound for Midway International Airport rumble regularly overhead.

Ricardo Palacios, a retiree who lives near the proposed tent city, said “our community, especially these people that live right here, they’re not going to be able to sleep peacefully” if it opens. Beverly Chan, another resident, said she worried the camp would be unsanitary and lead to an uptick in crime. Ms. Chan, a nail technician originally from China, also questioned the wisdom of housing 2,000 people in tents.

If “the city wants to build a house,” she said, “I don’t complain.”

With subfreezing temperatures lurking in the forecast, and with months of ice, snow and meteorological misery sure to follow, city officials have said there is no time for building houses. Barring setbacks in environmental testing, they expect to move forward with the tents.

Chicago has been overwhelmed in recent months by thousands of migrants arriving on buses and planes from border states, sometimes by Republican officials who have taken glee in putting “sanctuary city” and “welcoming state” pledges to the test.

Top Chicago and Illinois leaders, Democrats all, have feuded among themselves about who should be footing the bills while faulting the Biden administration for not sending more help. Nearly 12,000 migrants are living in city shelters, while about 3,300 more are sleeping in walkways at O’Hare International Airport, on the floors of police stations or outdoors. All the while, more buses keep coming.

“Some of them are under tarps,” Beatriz Ponce de León, a deputy mayor, told residents, which she said “is not a humane or a safe place for people to live.”

The proposed tent city, which some are calling a refugee camp, was no one’s first choice. But at the public meeting, officials described the facility, in which families would live in climate-controlled tents and have access to meals and showers, as their best option to stave off further crisis.

Some residents agreed. One man, now a teacher, described being embraced as a 9-year-old immigrant, and said, “I hope the neighborhood can find in their heart what I witnessed as a child.” A 92-year-old woman said what she was seeing “hurts me,” and called for kindness, peace and not being “against each other.”

Others pushed back. One woman, speaking through an interpreter, said she wanted migrants to have shelter, just not in her neighborhood. Some questioned whether the tents were humane. Many criticized the mayor’s office for not providing details sooner.

Conspicuously absent from the meeting were the voices of recent migrants, who so far have not moved into Brighton Park in significant numbers, though some are living at a police station east of the neighborhood and at a park field house to the south.

But toward the meeting’s end, the crowd quieted when a high school student named Julieth took the microphone. Speaking through an interpreter, she told how she had arrived from Colombia about a year ago, how her family was received warmly, how she was dismayed by insinuations that migrants were criminals.

“Please,” she told the hundreds who had squeezed into the auditorium, “don’t hate us for trying to find a better life.”