At the height of the surge in immigration last year, Cindy Garza found it hard to recognize the small Texas town of Garciasville, where she lives not far from the Rio Grande. Large crowds of people were often poking their fingers through the fence near the border crossing and screaming for help. Mothers and children kept trying to swim across the treacherous river. Once she came home and found a man who was fleeing the Border Patrol hiding under her bed.

Ms. Garza, a mother of four, has always seen herself as a Democrat, and voted for both Barack Obama and Hillary Clinton. But she has come to believe that President Biden’s softer policies on immigration have attracted the migrants from all over the world who have been seen spilling into the streets of her community. She is convinced that only a return of Donald J. Trump to the White House can restore order.

“When Biden won the last election, he said he was going to help people, and I saw a lot of people coming,” said Ms. Garza, who regularly crosses the local international bridges to visit and shop in Mexico. “I would see packs and packs of people. People saw it as a green ticket.”

Latinos all over the Rio Grande Valley, like many elsewhere in Texas, were once likely to be reliable Democrats, as Ms. Garza was. Now, widespread consternation over unauthorized crossings among residents along the border, where the majority of the population in most communities is Latino, could threaten support for Mr. Biden in what otherwise might be one of his key constituencies.

The Hidalgo County Democratic Party surveyed about 400 voters in southern Texas last year and found that even those who tend to vote for Democrats now support stronger border enforcement. Immigration reform and border security were ranked among the top 10 most pressing issues by respondents.

The results did not surprise Richard Gonzales, the county party chairman.

“You can ask anybody if there’s a problem,” Mr. Gonzales said. “Yes, there is. It needs to be addressed.”