Still, Mr. Miller has left a big mark, in ways both obvious and obscure. After two highly publicized failures, he helped craft a travel ban that passed court muster. A fervent critic of refugee programs, he has helped cut annual admissions by about three-quarters since the end of the Obama administration.

Writing in Politico, his uncle, Dr. Glosser, expressed an “increasing horror” at his nephew’s hostility to refugees and noted that their ancestor, Wolf-Leib Glosser, arrived at Ellis Island after fleeing Russian pogroms. Had Mr. Miller’s policies prevailed then, he wrote, the Glossers probably “would have been murdered by the Nazis,” as most in their village were.

With less fanfare, Mr. Miller has guided a series of policy changes that critics liken to building an “invisible wall.” The Migration Policy Institute, a nonpartisan research group, counted more than 100 of them, noting that “most have moved forward untouched.”

The Trump administration quadrupled the number of work site investigations. It slowed the processing of temporary H-1B visas. It imposed new performance measures on immigration judges, to encourage faster deportations.

Though Mr. Miller was often the driving force, many of these changes were longstanding goals of the restrictionist movement. “He comes from a community of people who’ve been working on this, some of them, since the ’90s,” said Roy Beck, the president of NumbersUSA.

Beyond the commas and clauses of government rules, Mr. Miller and Mr. Trump are trying to change something deeper: America’s self-conception as a land of immigrants. Mr. Trump is the son of an immigrant. Two of the three women he married are immigrants. Four of his five children have an immigrant parent. Yet his immigration agency rewrote its mission statement to remove the phrase “nation of immigrants.”

Mr. Miller even took to the White House briefing room to offer a revisionist view of the Statue of Liberty. Like many in his movement, he argued it should not be seen as welcoming immigrants because it was originally built for a different purpose (to celebrate political freedom) and that the Emma Lazarus poem hailing the “huddled masses” carries little meaning because it was added later.