Jeffrey’s situation is increasingly common. His father, Tomás Isidoro, 39, a carpenter, was one of the 46,486 immigrants deported in the first half of 2011 who said they had American children, according to a report by Immigration and Customs Enforcement to Congress. That is eight times the half-year average for such removals from 1998 to 2007.

Mr. Isidoro, wearing a Dallas Cowboys hat in his parents’ kitchen, said he was still angry that his 25 years of work in the United States meant nothing; that being caught with a broken taillight on his vehicle and without immigration papers meant more than having two American sons — Jeffrey, 10, and his brother, Tommy Jefferson, 2, who was named after the family’s favorite president.

As for President Obama, Mr. Isidoro uttered an expletive. “There are all these drug addicts, drug dealers, people who do nothing in the United States, and you’re going to kick people like me out,” he said. “Why?”

White House officials have said that under a new policy focused on criminals, fewer parents of American children are being deported for minor offenses. On Friday, the Obama administration also announced that hundreds of thousands of illegal immigrants who came to United States as children would be allowed to stay without fear of deportation. The policy, however, does not grant legal status, and because nearly half of the country’s 10.2 million illegal immigrant adults have children, experts say that inevitably more families will be divided — especially if deportations over all hold steady around 400,000 a year.

But for Jeffrey, the impact of his father’s removal in June last year was immediate. His grades dipped. His mother, Leivi Rodríguez, 32, worried that he had become more distant, from both his friends and his studies. Almost every day, Jeffrey told her he wanted to see his father.

So six months after her husband’s deportation, she sent Jeffrey to live with his father in Mexico, and she followed with Tommy a few months later. It was December when he arrived here in a hill town south of Mexico City, surrounded by fields of swaying sugar cane. On Jeffrey’s first night, he noticed something strange in his bed. “Dad, what’s that?” he asked.