There are a little more than two weeks between Juan, an electrician in the Bronx, and the date he cannot forget: March 21, 2017, at 8 a.m., when the federal government has told him to report for deportation.

Two weeks to decide: Avoid it, and try to preserve the American life he has built for a little longer, even as a fugitive. Go, and lose it all: his wife and son, his job, his apartment, his world.

“I would feel like an animal if I stay here and hide,” said Juan, 29, who asked that his last name not be used. “I want to prove that I can follow the laws. I want to make my case at this meeting, but I know that if I go, they’re going to deport me.”

In an immigration system mottled with escape hatches and hobbled by scant resources, Juan, who fled Colombia six years ago, is one of nearly a million people who have managed to linger in the United States despite having been ordered out of the country by an immigration judge — some of them more than a decade ago.