The state would be more willing to kick in more money to the School District of Philadelphia if the city followed through on Mayor Nutter's pledge to find the district about $100 million in new money, State Sens. Vincent Hughes and Shirley Kitchen wrote 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 leads the city's delegation in Harrisburg. Hughes, also a Philadelphian, is the ranking Democrat on the Appropriations Committee.

State lawmakers, in the midst of their own budget season, are exploring how much of Gov. Corbett's proposed cuts to education they can restore. The governor's proposed budget would cut state funding to the Philadelphia School District by $293 million.

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. He said the money would keep the district from slashing full-day kindergarten, transportation, and alternative schools, and would also aid efforts to keep classes small.

Council members have raised a number of complaints - there is no way to guarantee the district would spend any extra money on those priorities; the district has trimmed too little 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 does not have a budget by then, it cannot spend any money.

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

Nutter says shifting money from the municipal budget to schools would create "a painfully large gap" in the city's finances, his chief of staff wrote in another letter this week.

That stance has left Council bracing for a fight over a possible proposal to increase taxes. 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.

Nutter might have to reveal his hand in the next week. Just three Council sessions remain until the scheduled summer recess, and any proposal to raise taxes would have to pass through a committee vote first.

And Council has plenty of other business. Council and the mayor have dueling bills on reforming and ending the controversial DROP pension program, and there is a paid-sick-leave bill that has support on Council but 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.