NOGALES, Mexico — It was dinner time at the door to the United States, and on a spit of floor separating Mexico from Arizona, several families set out their plates, ripping tortillas and spooning rice and trying to ignore the indignities of life on the move.

“It’s weird,” said Brenda Aguirre, 23, who was planning to sleep that night with her children on a pink mat, curled around her belongings. Nobody, she pointed out, expects to end up here.

As the debate over the border rages in Washington, the flow of migrants has not stopped, and crossing points like this one are growing into informal bedrooms, washrooms, schools, kitchens and playgrounds for families waiting to request asylum in the United States.

Here in Nogales, officials come infrequently to interview people seeking entry, and so this place — a patch of ground between a fence and a line of people who already have permission to enter the United States — is fast becoming a symbol of life in transition. Most families wait here for days before being granted an initial interview with United States immigration authorities.