The state would be more willing to restore funding to the School District of Philadelphia if the city follows through on Mayor Nutter's pledge to find the district about $100 million in new money, State Sens. Vincent Hughes and Shirley Kitchen said in a letter.

The letter was sent Thursday to the mayor and City Council amid wrangling over how the city would generate that kind of cash for the schools.

Kitchen is the leader of the city's delegation in Harrisburg and Hughes, also a Philadelphian, is the highest-ranking Democrat on the Appropriations Committee.

State lawmakers, in the throes of their own budget season, are exploring how much of Gov. Corbett's proposed cuts to education they can restore.

More money from the city "would send a positive message . . . about our commitment to our children and will without question strengthen our hand in budget negotiations" with the governor and Republican leadership, Kitchen and Hughes wrote.

The question remains how Nutter plans to raise the $75 million to $110 million he promised this week. The money, he said, would keep the district from slashing full-day kindergarten, transportation services, and alternative schools, as well as aid efforts to keep classes small.

Council members have raised a number of complaints - there's no way to guarantee the district would spend any extra money on those priorities; the district hasn't sufficiently trimmed unnecessary spending to be asking for that kind of money; and funding the schools is primarily the state's responsibility.

Several Council members have said they would like to wait and see how much money the state provides, possibly setting up a game of financial chicken.

State budget officials have said they anticipate passing a budget before the June 30 deadline. If the city doesn't have a budget by then, the city can't spend any money.

District officials said they plan to pass a $2.8 billion budget by their May 31 deadline and then do an amended budget with any new state and city money.

Nutter doesn't want to shift money from the municipal budget to schools because that would create "a painfully large gap" in the city's finances, the mayor's chief of staff said in another letter this week.

That stance has left Council bracing for a fight over some sort of tax increase proposal. While many Council members have expressed a desire to help fill the $629 million gap in the district's $2.8 billion budget, they have been in near lockstep opposition to raising taxes.

There is support on Council for shifting the millage rate, which determines how property taxes are split between the city and the schools. While that would not affect taxpayers, a millage shift would require the city to make millions in cuts - an idea Nutter has rejected.

Timing-wise, Nutter might have to reveal his hand in the next week. There are just three Council sessions remaining until the scheduled summer recess, and any proposal to raise taxes would have to pass first through a committee vote.

And Council has plenty of other business to handle. Council and the mayor have dueling bills on reforming and ending the controversial DROP program, and there's a paid sick leave bill that has support on Council but that the administration opposes.

At Memorial Day, Nutter may have just a handful of votes for raising new school revenue, but there are six lame-duck members and lots of moving parts that could make deals possible up to the last minute.

Contact staff writer Troy Graham at 215-854-2730, tgraham@phillynews.com, or @troyjgraham on Twitter.