Gov. Dannel P. Malloy stood on a windswept lawn outside a branch library in Hartford’s North End for the second of five public events on his schedule Wednesday, a routinely busy day for a lame-duck governor whose to-do list includes stabilizing the state’s finances and saving its capital city from bankruptcy.

Hartford Mayor Luke Bronin and House Majority Leader Matt Ritter, D-Hartford, listened closely as Malloy, who came to announce long-awaited transportation improvements to Albany Avenue, was pressed by a reporter to say what Bronin and the city council realistically can expect in aid from a state with its own dire problems.

“They can be assured all of my expectations are realistic,” Malloy deadpanned.

On Wednesday, exactly five weeks until the General Assembly’s constitutional adjournment deadline, the best Malloy could do was to remind his audience of the priorities he established in his State of the State address in January and budget message in February: They include “greater support for urban environments.”

Exactly how much support might be available for Hartford — and under what terms, such as state oversight — is likely to be an element of the five-sided budget negotiations under way between the administration and the four legislative caucuses. The only consensus at the Capitol seems to be that a Hartford bankruptcy could be a bigger blow to Connecticut than the city.

“I do believe a bankruptcy in your capital city would be a black eye for Connecticut, for the legislature,” said Sen. Len Fasano of North Haven, the Senate GOP leader. “I don’t think for Mayor Bronin it would be a black eye. He walked into that. He’s not the architect.”

What Bronin walked into was a city that has run out of options.

Predecessors used refinancing gimmicks to balance recent budgets, and Bronin now faces several years of sharply escalating payments on the city’s debt. Squeezing more money out of the property tax is unlikely: Slightly more than half the property in Hartford, the home to three major regional hospitals and state government, is tax-exempt, and the city’s tax rate already is the state’s highest.

Bronin, who worked with legislative leaders as Malloy’s general counsel before his election as mayor in 2015, met Wednesday afternoon with Fasano to update him on the city’s fiscal condition. At Bronin’s invitation, Fasano previously had sent his budget staff to City Hall for a briefing and to examine the city’s books.

“I happen to have the highest regard for Mayor Bronin, I really do. I worked very well with him here,” said Fasano, a key player on the budget since Republicans won an 18-18 split in the Senate last fall. “I would love to do what I can to help Hartford get on its feet. I really think Mayor Bronin wants a different Hartford, a more fiscally responsible Hartford. But he’s been given a debt that’s a very tough thing for him to deal with.”

Bronin has proposed an 11 percent increase in the city’s $552.9 million budget, with debt service accounting for nearly half the $60 million increase. Health care, pension, payroll and legal costs represent most of the rest. He needs more than $40 million in aid from the state, a request landing on Malloy’s desk as state tax receipts are hundreds of millions of dollars off projections.

Bronin has obtained some concessions from the city’s workforce, and further state aid could come with an oversight panel that could demand further cuts and efficiencies. One of his immediate goals is to keep Hartford on everyone’s agenda as they work to balance the state’s budget.

“There are a lot of people at the State Capitol who understand you cannot have an economically strong region or even a strong state without strong cities,” Bronin said. “Hartford is not just the state capital, it’s the economic center for central Connecticut.”

Malloy proposed allowing cities to apply the property tax to hospitals, giving them a significant and stable new source of revenue. The cities now get payments in lieu of taxes from the state, but they do not fully reimburse cities for tax-exempt properties — and the payments often shrink in bad times.

The hospital plan failed to win significant support in the General Assembly.

On Wednesday, Malloy said Connecticut’s cities are at a tipping point.

“I think there is a body of people who don’t understand urban environments, and I think Connecticut has too long pursued a public policy of insufficient support for our urban environments,” Malloy said. “And that’s measured in both the ECS [education aid] formula, as well as other levels of support, particularly for communities that have a lot of non-taxable properties. I’m looking to address that.”

Ritter said he remains optimistic, saying that legislative leaders of both parties do comprehend the crisis.

“Do people understand Hartford? They do. I’ve talked to Len Fasano about it multiple times. I’ve talked to Themis about it,” Ritter said, referring to House Minority Leader Themis Klarides, R-Derby. “What the final answer is is still to be determined, but everybody cares. Everyone agrees that your capital city and all your cities need to be vibrant places for jobs.”

Bronin declines to say when the city would face its first default on debt payments, a potential trigger for bankruptcy.

“It would be a huge black eye on the state. It would affect the state’s credit rating,” Ritter said. “I think everyone gets that.”

House Speaker Joe Aresimowicz, D-Berlin, said Wednesday he still thinks a budget deal can be struck by the end of the session, if not by the end of May. But Democrats, whose small majority in the House gives them tenuous control over the Appropriations Committee, failed last month to find the votes to report a budget out of committee.

“We have five weeks to go,” Ritter said. “For a lot of people, that’s not a lot of time. In legislative time, it is.”