SAN ANTONIO — Donald J. Trump got Brenda Hernandez’s hopes up in 2016 when he indicated that he had a heart for young undocumented immigrants like her, who were brought into the country by their parents. But her hopes were dashed when Mr. Trump became president and ordered an end to the federal program known as DACA that shields her from deportation.
After the president’s latest announcement on Saturday — that he was proposing to end the standoff over the partial government shutdown by, among other things, temporarily extending that shield — Ms. Hernandez just shrugged.
“I don’t trust Trump — I don’t believe him,” she said as she hoisted her 3-year-old son onto a swivel chair at the D & H Beauty Salon in San Antonio. The blue-collar shop, with rows of wooden chairs in the waiting area, is a favorite among immigrants in the city. But in the hours after Mr. Trump’s White House address, his latest offer of an immigration deal was finding little support.
In exchange for $ 5.7 billion to erect a barrier along the border with Mexico, Mr. Trump said he would agree to extend protection for three years for the roughly 800,000 immigrants who benefit from the Deferred Action for Childhood Arrivals program, which covers people brought into the country illegally as children. The president held out the hope of similar relief for 300,000 immigrants living in the United States with temporary protected status, known as T.P.S., after fleeing earthquakes and other disasters in their own countries.
“I am here today to break the logjam and provide Congress with a path forward to end the government shutdown and solve the crisis along the southern border,” Mr. Trump said, calling his offer “a common-sense compromise both parties can embrace.”
But many of the clients waiting their turn for a $ 6 haircut or shave at the D & H salon, in a strip mall in the northern part of the city, greeted Mr. Trump’s announcement with skepticism, if not downright indifference. Most expressed deep reservations about a border wall, deeming it a waste of money.
Eliseo Castillo, 60, an undocumented immigrant from Mexico, said an extension of DACA’s protections from deportation, and its offer of work permits, could benefit his 26-year-old son. He said his son had relied on the program for years to get a driver’s license and a job and to live without the fear that even a minor misstep, like driving with a broken taillight, could land him in deportation proceedings.
But Mr. Castillo, a construction contractor who relies on a steady flow of workers from Latin America, said he wondered what would happen to his business if a reinforced border wall halted the flow of workers. He said he is already having trouble hiring enough laborers.
“The fact is, there is not an American who wants to mix cement, do carpentry and heavy work,” said Mr. Castillo, who employs 18 people to lay down foundations for houses in San Antonio’s expansive subdivisions.
Mr. Castillo, who wears cowboy boots and bluejeans and keeps his silver hair in a braid, has called Texas home since the 1980s. But he harbors no illusions about legalizing his status, at least as long as Mr. Trump holds the highest office in the land.
Waiting his turn for a haircut in paint-splattered trousers that gave away how he earns his living, Jose Ramos, 63, a naturalized American born in Mexico, said he had no faith that Mr. Trump, whose “favorite sport is blaming immigrants for everything, which is not right,” would ever keep his word.
“This isn’t a deal,” Mr. Ramos said. “Trump is just offering to give back what he already took away.”
Democrats in Washington have criticized the president for offering to extend DACA and T.P.S. protections, when it was he who had ordered those protections revoked. Some have called the offer a nonstarter because it did not include any long-term solutions, like a path to permanent legal status or citizenship for DACA recipients, who are known as Dreamers.
But many people in San Antonio never had much faith that such solutions were even possible with Mr. Trump as president.
Indeed, some in the city wonder how much the president knows about the border.
Speaking with reporters on Saturday, Mr. Trump cited the city as a place that had benefited from building a border barrier. “You look at San Antonio, you look at so many different places, they go from one of the most unsafe cities in the country to one of the safest cities, immediately, immediately,” he said.
But San Antonio is 150 miles from the border, and has no wall.
Alicia Alaniz, 47, the stylist working at station 7 in the salon, rolled her eyes and said that the only thing she could agree with in Mr. Trump’s statement was the notion that the immigration system was “broken.”
“We need immigration reform — it would benefit the country and everyone who lives here,” said Ms. Alaniz, a legal permanent resident who emigrated from Mexico. People just want to work the right way, and support this country that has brought them many blessings.”
President Obama introduced DACA in June 2012 as a temporary reprieve for young unauthorized immigrants, at a time when Congress was in a stalemate over immigration policy. To qualify for DACA protection, immigrants must have lived in the United States for much of their lives and meet certain other requirements, like passing a background check and completing high school.
On the campaign trail, Mr. Trump vowed to eliminate any program that Mr. Obama had created by executive action, including DACA, a stance that generated deep anxiety among the Dreamers.
But in December 2016, shortly after winning election, Mr. Trump softened his position.
“We’re going to work something out that’s going to make people happy and proud,” he told Time magazine. “They got brought here at a very young age, they’ve worked here, they’ve gone to school here. Some were good students. Some have wonderful jobs. And they’re in never-never land because they don’t know what’s going to happen.”
Once in office, however, Mr. Trump appointed one of the fiercest opponents of the DACA program, Senator Jeff Sessions of Alabama, as his attorney general. Mr. Sessions rescinded DACA in September 2017, but the action was challenged in court and has yet to take full effect, while the courts decide the program’s fate.
Without work permits provided under the program, young immigrants would face cascading, and possibly dire, consequences: They would lose their jobs, driver’s licenses and the chance to attend college at in-state tuition rates.
Friday was the last day the Supreme Court could accept an appeal and schedule any arguments on the DACA litigation in its current session, and the court let the day pass without addressing the Trump administration’s bid to kill the program. That ensures that DACA will survive at least until the court’s next session, which begins in October.
When the administration made its bid to end the program, “I worried about what I would do; I was so sad,” said Ms. Hernandez, who works these days for a casual dining chain known as Zoe’s Kitchen. But with the issue tied up in the courts, she said she has simply had to get on with her life. “Now, I don’t even think about it,” she said.
Her DACA permit expires in a year.