Before dawn Sunday, a former cook at the World Bank, an accountant from Moscow and eight other homeless Washingtonians awoke in the sanctuary of Grace Episcopal Church in Georgetown and stowed away their cots.

A few blocks north of the White House, coffee was brewing in another church fellowship hall at daybreak. A Sudanese man with a clutch of plastic bags was first in line to go inside and warm up.

By lunchtime, more than 400 homeless men and women — each with a story of loss — had come and gone from Franklin Square, where they picked up free sandwiches trucked in from congregations in the District, Maryland and Virginia.

Less than two weeks before the swearing-in of Mayor-elect Muriel E. Bowser, a homeless problem that exploded into the city’s public consciousness last year is again palpable on the streets of the nation’s capital.

The District’s main shelter for homeless families is at capacity, and a motel the city leased to serve as an overflow shelter is filling fast. A census last week showed rising numbers of homeless single adults, with more than 1,460 using emergency nightly shelters even before the bitter heart of winter sets in.

Timothy Lewis is a homeless man who often spends the night near Franklin Square. While he hopes there will be more money to help the homeless under the new mayor, he's not that optimistic that anything will change. (Michael S. Williamson/The Washington Post)

But the city’s official tally of whom it counts and whom it shelters tells only a fraction of the story.

Several hundred men and women are being fed daily, and scores are housed nightly, through a loose network of church ministries that have either sprung up or expanded in recent years as the city chose a tough-love approach with its homeless.

Organizers of the charity efforts say they are happy to provide the meals and beds. But they also warn that their ability to cover the District’s growing need is being stretched thin and cannot be sustained indefinitely.

More than 40 churches, synagogues and other houses of worship are circulating petitions that call on Bowser (D) to sign a covenant to make homelessness and affordable housing a top priority.

“We want the city to plan better and manage better,” said Ann Friedman, an organizer with Good Faith Communities Coalition, the interfaith group that is organizing the petition drive. “The city has the money, and we want to see this become a priority.”

Bowser won the mayoralty in part by distancing herself last winter from Mayor Vincent C. Gray (D), who was seen as taking a hard stance in pushing the city’s homeless to get their lives in order. She blasted Gray’s decision to use city recreation centers and partitions provided by the Red Cross to create makeshift and temporary shelters and to bunch families together in gymnasiums and auditoriums. Bowser called it “no way to treat” city residents and vowed to increase funding to support permanent housing.

But many at a gathering of church leaders and advocates for the homeless on Friday questioned whether Bowser and the D.C. Council — which last week approved a plan to spend at least $150 million on a new soccer stadium — are serious about addressing the city’s housing shortage.

“We’re still waiting — amen — for an administration in this city that will have the will to provide homes for all people,” said the Rev. Karen Brau, senior pastor at Luther Place Memorial Church on Thomas Circle.

Advocates for the homeless marched through downtown Friday carrying a wooden coffin to memorialize the 55 people who they say died in the Washington region this year from causes related to homelessness, including medical conditions aggravated by unstable living conditions and poor access to health care.

At least part of the city’s surge in homelessness has been blamed on gentrification and dwindling numbers of low-income apartments. While announcing the appointment of Polly Donaldson as her head of the Department of Housing and Community Development on Saturday, Bowser made it clear she sees a connection between the two.

Donaldson for a decade has led Transitional Housing Corp., which focuses on finding transitional housing for families coming out of shelters and apartments for homeless singles with mental health or substance abuse issues. She has also served on the city’s Interagency Council on Homelessness.

“I’m coming from an agency that has a foot in both” housing and homeless issues, Donaldson said.

As Joseph Brown, 45, packed up his cot Sunday at Grace Episcopal, he said he was relying on the roving five-month shelter provided by the Georgetown Ministry Center (GMC) rather than any service offered by the city.

“The city’s shelter is awful, horrible,” filled with violence and disease, he said.

Brown, who once worked for a temp agency as a grill cook at the World Bank, said he took a job as a dishwasher two years ago but lost it to a younger worker. The native of Tanzania said he hasn’t been able to make enough to keep a roof over his head since.

This year, Brown is hopeful again. He was one of 10 homeless people accepted into the roving shelter, which involves churches in Georgetown setting up cots in vestibules and multipurpose rooms to house people for rotating two-week intervals. Meals are provided by parishioners. The GMC has a small office where guests can shower, do laundry, receive mail and use computers to apply for jobs.

It has a track record of helping most of the 10 people it accepts each winter secure permanent housing by the time the five-month period ends.

Vaughn McCants, 30, who went through the center’s program last year after a breakup and alcoholism left him homeless, said the church ministry did something no city shelter could have: “I never felt before that there were so many people out there willing to help somebody they never met.”

He is now a music student at the University of the District of Columbia. He said he thinks about his experience on the street every day and avoids offers of part-time work as a bartender so he can stay away from alcohol.

“Success? It’s not over,” he said. “I could see how that journey gets started. It got started in me, and I had to take control of myself and not give up.”