Shortly after David R. Small took over as chief executive of D.C.’s United Medical Center last year, a woman at a community meeting gave him some unwelcome news about the facility he’d been hired to run.

“It was,” Small recalls being told, “the hospital where you go to die.”

The 354-bed hospital on Southern Avenue SE has long suffered from a dismal reputation as a hospital of last resort, an image buttressed by long-standing and well-publicized financial woes and its location, in one of the region’s most concentrated pockets of poverty.

But nearly 18 months into a crash turnaround effort, there are encouraging signs at the hospital. Although United Medical Center won’t be mistaken for Johns Hopkins anytime soon, patient volumes and billings are up, doctors are joining rather than fleeing the staff, and, for the first time in at least a decade, there is more than sufficient money in the bank.

Last month, the hospital announced that it will not require a government operating subsidy for the first time since the District seized control of it in 2010 — achieving a key goal of the turnaround ahead of schedule.

Small, a veteran health-care administrator hired by the city’s turnaround contractor, Huron Consulting Group, said perceptions of the hospital are starting to change: Patients are coming to United Medical Center by choice, and liking what they see. “We need to win our market back, and we’re starting to do that,” Small said.

But the story on Southern Avenue is not yet a fairy tale. While key indicators are improving, the hospital remains housed in a five-decade-old building that is increasingly expensive to maintain. A proposal from Mayor Vincent C. Gray (D) to build a smaller but entirely new $335 million hospital at the nearby St. Elizabeths campus has been met with skepticism from the D.C. Council, which removed some of the funding for the plan.

The ultimate goal of partnering the hospital with a larger private owner or operator has yet to be reached, or even proposed, as the clock ticks on the Huron contract, which is set to expire in March.

C. Matthew Hudson, chairman of the hospital’s board, said Friday that a search for a new chief executive to take over the hospital in March has been abandoned, and city officials are contemplating extending Huron’s $12.7 million contract in case a partner cannot be recruited.

“We believe we need time, just a little bit more time,” Hudson said.

The process of recruiting a suitable private partner has been complicated by the pending mayoral election, since the next mayor’s approach to key questions about the hospital’s future is largely unknown.

“Our partners we’re seeking to talk to are a little nervous,” said Hudson, who also is the pastor of nearby Matthews Memorial Baptist Church. “They don’t know what the next mayor will do, because they don’t know who the next mayor is.”

Mayoral candidate David A. Catania, an at-large council member who chaired the Health Committee from 2005 through 2012, moved aggressively to stabilize the hospital when it was foundering under private ownership. Catania (I) backed the city takeover in 2010, and while skeptical of the need to recruit a turnaround firm, he supported the Huron contract.

Catania has, however, opposed the proposal to build a new hospital, saying a partner can be recruited to run the existing hospital.

A spokesman for Democratic nominee and Council member Muriel Bowser (D-Ward 4) said Bowser is “committed to a full-service hospital east of the river.” The spokesman, Joaquin McPeek, suggested the hospital bailouts arranged by Catania amounted to “a Band-Aid, not a fix” and said Bowser has not ruled out a new hospital. “If the right strategic partner came along and proposed a new site, she’d entertain that,” he said.

Carol Schwartz, the former at-large council member running as an independent, said in a statement that her commitment to an east-of-the-river hospital “is ever-present and long-standing,” adding that she is open to proposals involving a new site. She, too, is dismissive of Catania’s efforts on behalf of the hospital, pointing to her warnings in 2007 that it could “become a bottomless pit” for city funding. “Obviously and unfortunately, I was right,” she said.

The good news is that, by the numbers, the hospital now has a significantly better story to tell its potential partners.

“We are much more attractive today than we were a year ago,” said Michael E. Davis, the hospital’s chief financial officer, who reports to Jeffrey S. DeWitt, the city’s CFO. “The goal for 2015 was to not depend on any District support for operations, and we are there.”

Before Huron’s arrival, United Medical Center had as little as four days’ cash on hand and was juggling its bills. According to the most recent quarterly figures, from June, the hospital has 80 days’ cash on hand and bills are being paid on time. The hospital used to struggle to collect revenue from patients, but collections now are trending over 100 percent, meaning new bills are getting paid, plus some old ones, too.

The hospital remains overly dependent on emergency-room traffic to drive patient admissions, but its ER is busier and operating more efficiently. Thanks to an effort to decrease offload times, more ambulances are bringing patients to United Medical Center.

More doctors and new types of doctors have joined the staff, and a new vice president has been hired to focus on medical recruitment. Key specialties such as cardiology, orthopedics and urology are staffed for the first time in years, and the hospital is adding technology to draw patients who need MRIs, low-dose mammograms and advanced wound care.

Perhaps most crucially, steps have been taken to execute elements of a long-term strategic plan that calls for expanding focus on ambulatory and outpatient care. Before leaving the United Medical Center emergency room, patients stop to speak to a medical “concierge.” That person directs them to the growing corps of primary-care and specialty physicians on the hospital campus in a bid to both reduce ER visits and encourage connections between the hospital and the public.

In the coming year, the hospital plans to open two primary-care centers in D.C. neighborhoods east of the Anacostia River, making good on long-standing plans to better serve the community.

The hospital building, constructed in the late 1960s as the Cafritz Memorial Hospital and later renamed Greater Southeast Community Hospital, remains something of an albatross. The city has pumped more than $100 million into the physical plant since 2007 — investments that are readily apparent in some ways, including new elevators, brighter hallways and the advanced medical equipment.

But like an aging car, Small said, the hospital will become increasingly expensive to run, and the operating gains will hardly be enough to cover those costs. The city anticipates $24 million in capital needs in the next fiscal year, with the new surplus from hospital operations supporting only about $3.5 million.

Without a new building, Gray has said, the city will remain on the hook for capital outlays indefinitely, even if management has the hospital running like clockwork.

“You’re going to end up putting lipstick on a pig, said Christopher Murphy, Gray’s chief of staff, who has been engaged in the discussions over the hospital. The council’s decision not to immediately fund a new hospital, he said, has “made it more difficult to identify a strong partner.”

While the debate simmers over whether a new hospital is needed, management is moving forward with renovations to patient rooms and nurse stations, an expansion of the emergency room and improvements to public spaces.

Potential partners “are interested,” Hudson said, adding that the most serious offers involve “operating management agreements” that would leave the city responsible for capital needs.

Small said he’s confident a partner will be found.

“We are showing . . . that a full-service hospital in this part of the District is an attractive business proposition,” he said.