The leading D.C. mayoral candidates, Muriel Bowser, David Catania and Carol Schwartz, meet during a debate last month at American University in Washington. (Cliff Owen/AP)

When the new mayor takes office in January, he or she will probably step into a crisis.

An estimated 850 families are projected to be homeless this winter. That’s a 16 percent increase from the year before, when an earlier surge sent city officials scrambling to fulfill their legal obligation to provide shelter when temperatures dip below freezing.

The city will confront this increase with fewer spaces at its main emergency shelter. Over the summer, 40 rooms were deemed unsuitable for use at the old D.C. General Hospital campus — and serious questions remain about whether the dilapidated facility should be used at all.

The budget is also $10 million short of what is needed to house the homeless, according to Kate Coventry, an analyst at the D.C. Fiscal Policy Institute.

How this complicated problem is handled is likely to be the first test — and first overt display of leadership, or lack thereof — for the next mayor.

Looking at where key candidates stand on pressing issues facing Washington.

All three major candidates — D.C. Council members Muriel E. Bowser (D-Ward 4) and David A. Catania (I-At Large) and former council member Carol Schwartz, an independent — have agreed that the city needs to adopt a more caring approach to dealing with its homeless. The current administration’s policies, including reducing the time and length of rent subsidies, have been criticized by advocates as overly harsh.

Still, the candidates offer three distinct approaches, targeting different facets of the city’s homelessness crisis and its shortage of affordable housing.

Bowser, who is leading in the polls, plans on improving upon a strategy known as “rapid rehousing” to find more apartments for homeless families while attempting to close down the D.C. General shelter.

Catania offers a more radical approach by expanding permanent rent supplement programs. He said he is unsure whether the shelter needs to be closed.

Schwartz said she thinks the city should “muddle through” this winter until it can either remodel D.C. General or build another large-scale facility.

“This is a big problem, but I’m optimistic that it can be solved with bold leadership and a heart for these families,” said Patricia Mullahy Fugere, the executive director for the Washington Legal Clinic for the Homeless. She would like to see more creative approaches to the issues. “So much of [the debate] stops short of where it needs to be if we are going to be serious about addressing this homeless crisis, and the affordable housing crisis.”

Here’s how the system works: When temperatures dip below freezing, homeless families line up at the Virginia Williams Family Resource Center to seek shelter. Caseworkers assess their needs before providing shelter, likely in a motel or at D.C. General. The families reside there until they can find housing on their own or be placed in the city’s rapid rehousing program, which guarantees heavily subsidized rent for four months. Families can reapply for the program for as long as a year.

D.C. mayor quiz

The city’s hypothermia plan lists 369 shelter rooms to serve the projected 850 families who will be homeless this winter. Case managers must work to get families out of shelter and into housing as quickly as possible, making room for new ones.

Failure to do so could lead to a similar situation to last winter, when the city said it had no other option than sending families to Maryland hotels. The city also sent families to recreation centers, a process that was deemed illegal.

Improving the ‘exit rate’

To prevent bottlenecking, city officials are trying to improve the homelessness “exit rate” to 100 families a month. The exit rate has steadily increased over the summer to about 64 families a month.

There are roadblocks to reaching the exit-rate goal. First, some families are unwilling to leave their shelter if they are not guaranteed a permanent subsidy. Second, some landlords have been hesitant to accept families using rapid rehousing vouchers because it guarantees rent for only four months. Third, when the rapid rehousing voucher expires, families frequently have difficulty affording market-rate housing and can wind up homeless again.

Each candidate targets a different part of that system. Bowser’s plan addresses the exit rate by trying to build relationships with landlords, potentially guaranteeing them rent for an entire year in exchange for participation in rapid rehousing.

“It’s important that we be specific about this,” Bowser said. “We’ve talked to landlords, and half of them don’t know what rapid rehousing is — they don’t know if it’s for months, a year, two years. We have to be able to give them assurances.”

In Bowser’s plan, an increasing reliance on rapid rehousing would help to facilitate the closing of D.C. General. Instead of going to a shelter or motel, families could just be placed in housing.

Bowser declined to project a date when she thought she could close the shelter, but her policy papers have stated that she thinks she could end family homelessness in the city by 2018.

Bowser’s long-term plan, like those of the other candidates, is to invest more in affordable housing.

She vowed to fix the troubled New Communities Initiative program, a housing strategy for revitalizing poor neighborhoods without losing any units of low-income housing. She also said she would mandate that any public land redeveloped for housing be 20 percent affordable, as well as guarantee $100 million a year to help developers finance projects that would bring affordable housing into the city. All of these plans are tweaks to the system set into motion by Mayor Vincent C. Gray (D).

‘Absence of leadership’

Catania wants to review the city’s housing needs annually, at all level of incomes, and use those reports to inform how officials go about developing new housing.

The homelessness and housing crisis is “the direct result of an absence of leadership,” he said. “We need to immediately address the issues of how we do things, and what we have not done.”

Unlike Bowser, Catania said he thinks rapid rehousing “only delays the inevitable” because some families will never be able to find affordable housing in the District. He said he’d rather spend money on emergency rental assistance to help families get through unstable periods and on funding permanent housing vouchers.

Catania said more research needs to be done on whether closing the D.C. General shelter is the best option. He said it might prove too difficult to find another shelter.

As for this winter, Catania said poor leadership has left the city with “terrible choices” that cannot be avoided. There will be little choice but to use motels outside the District as emergency shelters, he said.

Schwartz said she would focus on the relationship between case managers and homeless residents. She wants to invest more in prevention services and job training, reimagining D.C. General as a one-stop shop for support services.

She said she thinks families can comfort each other if they are around families who are going through similar struggles. “They can learn from one another and help one another,” Schwartz said.

Schwartz also wants to set aside $150 million each year — $50 million more than Bowser — to help developers finance mixed-income projects through the city’s Housing Production Trust Fund, as well as devise stiff penalties for developers who don’t deliver on their promises to build housing units.

Despite her tough talk for developers, Schwartz agreed with Catania and Bowser that the city needs to adopt a softer approach.

For Fugere, that would be a welcome change.

“I know this sounds squishy, but what we need most is a conversion of heart,” she said. “It would be nice to see the new mayor acknowledge that there is a true need in this community, rather than an assumption that families are trying to game the system.”