Vote against pensions, Corbett said, and city schools will end up at least $96 million short of the $135 million in additional funding Mayor Nutter said is needed to open the doors in September.
"The Philadelphia delegation has the ability to help far more than they have," Corbett said in an impromptu news conference with reporters in his Capitol office. "If there is a positive pension reform vote there will be a cigarette tax for Philadelphia."
Corbett added, "It's in their hands."
Nutter, who was in Harrisburg Sunday with School Superintendent William Hite, meeting with the governor and lawmakers, called the tactics "political horse trading at its worst."
"The schoolchildren of Philadelphia should not be held hostage," he said, "to matters that have nothing to do with the education of children."
The drama played out in the halls of the Capitol as House and Senate lawmakers reconvened for an unusual weekend session a day before the June 30 budget deadline.
The governor's comments came as the Senate was preparing to vote on the House-approved $29.1 billion budget with no new taxes. Instead, an estimated $1.5 billion budget gap would be filled with one-time fund transfers, suspension of grants and tax credit programs, and delayed payments.
The Senate is expected to vote on the budget Monday afternoon, with a final House vote later Monday ahead of the midnight deadline.
Meanwhile, Nutter and Hite sounded the alarm that without additional funding, class size in the city's 202 schools would jump to 41 students and 1,300 teachers would be laid off.
The $2-per-pack hike to the cigarette tax - approved by Philadelphia City Council but needing legislative authorization - would bring in an estimated $80 million, which Hite and Nutter say would bring the city close enough to plugging the hole in the $2.6 billion school budget.
And that presumes approval of the extra $39 million that Corbett proposed for the city in his February budget address, but which had not been finalized by late Sunday.
As the clock ticked toward Monday at midnight, Corbett, who said he would not sign a budget without the pension changes, recognized he lacked sufficient GOP support. So he and House GOP leaders turned to Philadelphia House Democrats with the deal for city schools.
The Philadelphia House delegation's leader, Rep. Cherelle L. Parker, said Corbett has a constitutional and moral obligation to ensure all students are educated, including those in Philadelphia - a school district he in effect controls through his appointments on the School Reform Commission.
Recently appointed School Reform Commission chairman Bill Green, who also came to Harrisburg Sunday, said both sides have to compromise.
"We need funding for Philadelphia schools and pension reform to help all schools over time," he said. "I'm not sure people understand the consequences."
But a visibly angry Nutter decried the coupling of pensions and school funding, comparing the treatment of Philadelphia's schoolchildren to that of damsels in distress in the silent movies.
"It is a sad day in public service that we find children being held on the railroad tracks awaiting some rescue to come from somewhere that has nothing to do with them," he said.
Asked if he was urging Philadelphia lawmakers to support the pension legislation, Nutter said, "I'm asking them for a vote of conscience to ensure that public schools open in Philadelphia on time and safe."