"We've played our hand," Majority Leader Curtis Jones Jr. said. "This is the best effort we could put forward."
The action now shifts to Harrisburg, where state legislators are dealing with a complex swirl of issues, including the commonwealth's own $1 billion deficit.
Philadelphia's leaders are hoping to extract from that morass a number of measures that could, potentially, put the School District back in the black.
Primarily, the city is seeking state permission to charge a $2-a-pack, Philadelphia-only tax on cigarette sales.
There, again, the story rings familiar: A bill to enact the cigarette levy stalled last year in the Republican-controlled General Assembly, where many members were elected on antitax pledges. But there is optimism that a deal can be struck this time, if the GOP leadership needs Democratic votes to balance the state's books.
Much like last year, the fate of the cigarette tax and any state funding for Philadelphia's schools is likely to come down to the wire on June 30, the end of the fiscal year.
"You never know until the wee hours of the deadline what's going to come together," said Councilman James F. Kenney. "It's been that way probably since before I was born."
Council, meanwhile, is on schedule to pass the city's budget for the new fiscal year - $4.5 billion, counting on proceeds from the proposed sale of the Philadelphia Gas Works - at its Thursday meeting, on the eve of its 12-week summer recess.
Even if Council calls another meeting June 26, the city is sure to finish its budget business well before the state - and well before the fate of the cigarette tax and any state school funding is known.
"For sure we're all waiting with bated breath to see what the state is going to do," said Councilwoman Blondell Reynolds Brown, the majority whip. "There's a lot of shuttle diplomacy going on."
Councilwoman Maria Quiñones Sánchez said, critically, that Council was playing "gamesmanship with Harrisburg."
"We're going to wait for Harrisburg, and we're going to be right where we were last year, looking for Plan B," she said.
If the cigarette tax isn't approved, Jones said, "there is no acceptable Plan B."
"We are finding quarters in the couches to take care of our children," he said. "It's time for the state to help us out."
(Jones also noted his own efforts to dig out those quarters: A bill he sponsored this year to raise parking-meter rates in some commercial corridors is expected to bring an additional $7 million next year to the schools.)
The city is not permitted to enact new taxes after June 30. So, once the new fiscal year starts July 1, any additional funding for the schools would have to be plucked from the city's budget, which already has a number of unresolved demands on it.
For one thing, Pete Matthews, president of AFSCME District Council 33, reminded Council on Thursday that his 10,000 blue-collar municipal workers have been waiting more than six years for a raise.
Many Council members have been consistently critical of the School District's financial stewardship this year and in previous years.
And few would be happy with dipping into the city's fund balance or making cuts to deliver more money to the district in the fall.
But even those who have expressed misgivings know the district is operating on a shoestring of staff, nurses, and counselors, a situation Jones called unacceptable.
"If the cigarette tax doesn't happen, we come back in September and make some more adjustments," Kenney said. "I'm willing to do that."
If Council is called upon to craft a Plan B, "we're going to have to put our heads together again and deliver again," Brown said.
"I'm confident that we will," she said. "There are too many of us in here who are not OK with not giving them what they need."