Dozens of attorneys, advocates and shelter operators on Friday cast the District’s $124 million homeless operation as a system in disarray, failing to help the city’s most vulnerable and wasting money — and the administration of new Mayor Muriel E. Bowser (D) largely agreed.

“We’re operating in crisis mode,” said Kristy Greenwalt, Bowser’s new homeless czar. “Not only is our response inadequate and inhumane, but it is also very expensive for taxypayers,” Greenwalt said. “The costs don’t just appear in the [Department of Human Services] budget. They are hidden in agency budgets throughout the city: the budget of the Metropolitan Police Department, the budget of Health Care Finance, the budget of the Department of Corrections, just to name a few.”

Greenwalt’s testimony capped a six-hour hearing led by D.C. Council Chairman Phil Mendelson (D) that amounted to the most open, and at times tense, airing of the city’s homeless crisis in years.

As the city surpassed 4,000 people in shelters and appeared on track for its largest homeless count in decades, however, the hearing routinely raised more questions than it answered.

City contractors and nonprofit groups charged with matching homeless men and women with transitional housing described a system that has all but stalled during the changeover between mayoral administrations.

Over $7 million in funding that former mayor Vincent C. Gray (D) and the D.C. Council approved last spring for apartments for homeless veterans and a new triage system to assess the needs of the homeless has remained unspent, compounding the number left to fend for themselves on city streets this winter.

Attorneys for the poor also testified that a program for getting homeless families out of shelters and into temporary apartments is backfiring, leaving families in eviction court with apartments they cannot afford — and again teetering on the brink of homelessness.

“It seems we’ve thrown money at different places and maybe we haven’t thrown it in the right place,” said Mendelson, who re­organized the council this year to give his office more direct oversight of the city’s homeless budget.

Laura Zeilinger, Bowser’s acting director of Human Services, who left a position coordinating homeless services nationwide for the Obama administration, said she believes all of the problems are solvable, but she promised no magic and no quick fix.

“The needs are great, and we have much work to do,” Zeilinger said, adding that she and Greenwalt hoped to have a plan to present to the council within months.

Council member David Grosso (I-At Large) fired back that that was too slow, and would not give the council a chance to rearrange funding in the budget that will cover programming for next winter.

“I’m willing to give you all the money that it would take — don’t wait, you might lose our support,” Grosso said. “You never know. A new soccer stadium, a new baseball stadium might come along. You can’t wait on this. This is an emergency right now.”

Mendelson was more measured and said he was willing to give Bowser’s team time to prioritize spending.

But he also said he expected the administration to develop a plan that could be implemented in the next annual budget.

The council chairman also zeroed in on $600,000 that Bowser has frozen for adding new case workers to the city’s family homeless shelter at the former D.C. General Hospital campus.

He pressed Zeilinger on why the new mayor could justify not spending such a small amount that could help so many.

Zeilinger said none of the 230 families at D.C. General or over 400 families now placed in overflow motel rooms across the city are going without case workers to help connect them with city services.

“We need just a little bit more time to look at the need,” Zeilinger said. “We needed a moment to assess if we are really providing the level of service that is needed.”

Mendelson said Bowser was creating an early rift with the council over the funding, which he noted was specifically added by the council last year after hearing testimony from advocates about the living conditions at the shelter.

Mendelson told Zeilinger that he was irritated by the funding freeze. Take that message “back to the executive,” he said.

The exchange came two days after Bowser had told a crowd of volunteers, who fanned out across the city to count the District’s homeless and to offer them aid, that her administration would “end chronic homelessness.”

That broad proclamation was more ambitious than a campaign promise that Bowser had made to end family homelessness in the District by 2018.

Greenwalt and Zeilinger confirmed that ending homelessness in the city is the goal, but both said they were working on a “feasible timeline” to achieve the overall objective. They described an ideal system as one that would spend the bulk of city taxpayer dollars for homeless services on prevention and short-term aid, and on affordable housing rather than shelter.

Greenwalt also said there was little the administration could have done since Bowser won election to have turned the tide before this winter.

“There is really no amount of planning in a very short window, four- to six-month window, that could have substantially reduced the number of families seeking assistance,” Greenwalt said.

“The need in our community is great . . . and we are spending a tremendous amount of taxpayer dollars to simply manage homelessness,” Greenwalt said. “We need to reorient our thinking away from managing it to truly ending it.”