Finance Director Rob Dubow said he would have something by early May.
"We're kind of ticking on this clock here," Clarke said, later asking about the date. "This is what, the 23d?"
"It is," Dubow said, offering nothing further.
"All right," Clarke said. "I can see I'm not going to get a response out of that one."
Clarke said in a later interview that Council's main priority was dealing with Nutter's property-tax plan, the Actual Value Initiative (AVI), and he noted that budget hearings were likely to end this week without a blueprint for getting the $60 million.
"Until that happens, I'm not going to have the level of conversation that needs to be had with Council members," Clarke said. "I haven't gotten a sense that there's an appetite for any additional taxes from any source."
School Superintendent William R. Hite Jr. has made clear the stakes of inaction are dire. Hite, who is expected to testify Monday along with School Reform Commission Chairman Pedro A. Ramos, is counting on that money, plus $120 million from the state and concessions from the teachers' union, to close a deficit in his budget of more than $300 million.
This month, Hite painted a "catastrophic" picture in which the district would have to lay off 3,000 employees and cut sports, summer school, librarians, and counselors.
He reiterated Friday that he would rather ask for money to expand art and music programs; instead he's looking to fund basic education.
"We're asking for a lot of money just to maintain the status quo," he said. "It's a bad position to put Council in, quite frankly. It's really important to acknowledge the contributions that City Council has made over the past two years."
The bulk of the city money going to the schools comes from three sources - property taxes, which are split between the city and schools; the use and occupancy tax on businesses; and the liquor-by-the-drink tax.
They contribute about $810 million, less than a third of the district's $2.7 billion budget.
Given that Council has raised property taxes in the last two years for the schools, and considering the discontent among some homeowners seeing increases this year under AVI, that seems an unlikely avenue for new money.
Councilwoman Maria Quiñones Sánchez has introduced a bill that would raise the use and occupancy tax, mostly on larger businesses likely to get lower property taxes under AVI.
Her bill is the only one currently on Council's docket that would provide money for the schools. Sánchez said the administration was still analyzing the proposal, but "they realize there's the potential to capture some dollars there."
She also suggested the mayor trim as much as $25 million from the budget he proposed to Council, which included $18 million in new spending.
"The mayor has to show us how much he's giving us from his proposed budget," Sánchez said. "Because he cannot expect us to do the heavy lifting by ourselves."
Raising the 10 percent liquor-by-the-drink tax has been touted as a possible tactic, but the city would need the state's permission to do so, which Councilman James F. Kenney described as unlikely.
(The drink tax itself was once a controversial idea to prevent the schools from making cuts during a budget crisis in 1994.)
Kenney complained about not getting a formal request for more money or an explanation of the amount sought.
"Where does $60 million come from? Why not $50 million? Why not $70 million?" Kenney asked. "If the mayor is going to ask, he should lead and be specific."
Nutter's spokesman, Mark McDonald, reiterated that the administration was working on the problem.
"We propose to work with Council members to come up with a solution, and that's what we're doing now," he said.
Nutter's previous efforts to lead on this issue met stiff resistance in Council.
In 2011, he suggested creating a new revenue stream for schools with a sugary-drink tax that he said would collect $100 million. Council never took a vote on the proposal, and instead raised $53 million for the schools, mostly through a property-tax hike.
Last year, Nutter suggested raising $94 million in property taxes during the change to AVI; Council delayed AVI for a year and raised $40 million for the schools through property and use and occupancy tax hikes.
Council members for years have complained about state cuts to education, considering the governor controls three of the five appointees to the School Reform Commission.
Councilman W. Wilson Goode Jr. said if more city money doesn't come with additional state support, "then . . . what are we buying?"
"Under every scenario, even in the School District's plan, it appears we'd be paying more and still getting less," he said. "If you can't invest enough money to have some significant impact, then the question is whether you're throwing good money after bad."
Clarke asked Dubow last week whether any city contributions could be contingent on state help, and there's a sense that Council could play financial chicken with the General Assembly to make sure the state acts as well. Both have to pass their budgets by June 30.
Clarke also has criticized the mayor for not addressing in his March budget proposal additional funding for the district. Although the district didn't complete its own budget until this month, predicting the schools would need more money wasn't a stretch.
"Were they aware there would be this level of shortfall much earlier?" Clarke asked. "I find it hard to believe somehow they weren't aware they were going to have this problem."
Contact Troy Graham at 215-854-2730, email@example.com, or follow on Twitter @troyjgraham.