At 7 a.m. Tuesday morning, as temperatures hovered around freezing and the skies threatened snow, Melissa Castro and Daniel Young bundled up their two babies, crammed most of their belongings into three duffel bags and stood outside a dark D.C. government building.

For more than an hour, Castro and Young waited with about two dozen other families with young children for the daily opening of the Virginia Williams Family Resource Center, the one place in the city where caseworkers assess which impoverished families are truly homeless and, thus, will get a coveted spot in a full-to-bursting family shelter system.

Castro, 19, pulled a wool Nike hat down over the ears of her 2-year-old son, Jayden. She nervously eyed 1-year-old Kaylee — wide-eyed, red-cheeked and silent in her car seat — and carefully tucked a worn towel around her.

“We have nowhere else to go,” she said.

Already, 288 homeless families fill every single room at the D.C. General family shelter, city officials confirmed. An additional 125 families fill every apartment in the city’s only other family shelter. As of Friday, 326 homeless families had been put up in budget motels around the city and in Maryland.

In the first few months of this cold season, the number of families that have gone to Virginia Williams because they are homeless or on the brink of homelessness has increased 30 percent from this time last year, said Michele Williams, chief of systems integration for the nonprofit Community Partnership for the Prevention of Homelessness.

“In the past few years, we’ve lost hundreds and thousands of affordable housing units. And this is what you see as a result,” Williams said. ‘People are getting displaced.”

By 8 a.m., as Castro and Young huddled in a corner near the building entrance to stay warm, a city official had appeared to tell the crowd that the resource center wouldn’t open because of the weather. The official, who declined to give her name, suggested that people call the 24-hour emergency shelter hotline.

Every adult in the crowd pulled out a cellphone and began to dial.

Young, 20, explained that he and Castro had been homeless for about three years, drifting among relatives and friends, and now had no where to go. They both have high school diplomas, but their low-wage jobs — she works for a temp agency and he, until recently, for Cosi — and inconsistent hours, complicated by a lack of child care, don’t add up to enough to cover market rent.

He ended the call and shrugged. “They said to sit tight. They’ll call back.”

A woman who overheard the conversation scribbled her phone number on a piece of paper and handed it to Castro and Young. “I’m about to be evicted,” she said. “But if worse comes to worse and you don’t get into shelter, give me a call.”

Keshia Roberson, 35, her seven children gathered around her with all their belongings stuffed in plastic bags, was at Virginia Williams on Tuesday to explain that she was homeless only because her apartment burned down in September. Although the Red Cross put her and the children up in a motel for two weeks, she said, she couldn’t leave children younger than 18 on their own there. To care for them, she missed work as a janitor at Children’s National Medical Center, and she was fired.

With no money to pay for another apartment, she and her children began sharing a two-bedroom apartment with her cousin, her cousin’s husband and their two children. When a neighbor complained to the landlord that the apartment was overcrowded, Roberson said, she knew that she had to go.

Roberson would call the hotline 14 times in less than 24 hours. “Well what am I supposed to do?” she said angrily into the phone. “It’s cold out here!”

By 10 a.m., as snow started to fall, Roberson and her children, and later Castro and Young, decided to wait at a nearby McDonald’s on New York Avenue. “Here,” Castro handed Roberson a plate of pancakes her son hadn’t finished, as Roberson’s children eyed the syrup-soaked cakes hungrily before gobbling them up.

Within a few hours, Castro and Young had been given shelter at a Motel 6 on Georgia Avenue, just a few blocks from the Maryland line. And a van had come to take Roberson and her children to D.C. General.

By early afternoon, Young had found the thermostat in the motel room and turned it to a comfortable 70. Castro peeled the snowsuits off the two children and handed them cheese puffs as they jumped on the single king-size bed in the bright orange room.

Across town, at D.C. General, Roberson and her children — their fathers are either in jail or are not part of their lives — were assigned cots in what, until that afternoon, had been a small activity room on the fourth floor.

“We got a roof over our heads!” son Joshua, 10, called out as he sat on the floor eating pasta and meatballs that shelter workers had brought.

Roberson unwound the black turban she keeps wrapped tightly around her head to hide all the hair she’s lost in the stress of the past few months. She watched the snow pelt the windows.

“I’m not even hungry,” she said, handing her food to her children and slumping against the wall. “I think I’m just going to rest.”