HARRISBURG, Pa. (AP) -- June is crunch time in the state Capitol and the challenges in front of Gov. Tom Wolf are becoming clearer in the Democrat's first go-round with budget negotiations. For Wolf, who took office in January, it will be perhaps the biggest test yet of his mettle, and an important sign of how successful he will be the rest of his term in persuading the state Legislature's huge Republican majorities to support his priorities. The last few days provided something of a preview of the battles awaiting Wolf's administration and how it might handle them. It ruffled Republican feathers in the Capitol this past week with a bare-fisted attack on the Senate Republicans' top priority: a bill to scale back pension benefits for future and current public school and state government employees. And Wolf, in an open letter that brimmed with frustration, made plain how little headway he has made in winning over opponents to a tax increase on Pennsylvania's booming natural gas industry, a source of money Wolf is counting on to pump more money into public schools. Wolf's press secretary, Jeff Sheridan, maintained that the administration had made no deliberate decision to raise its voice or send an unmistakable message to Republican lawmakers and business advocacy groups that have shown little interest in Wolf's ambitious agenda. "I don't know that I think our tone has changed," Sheridan said. "These are issues that we've supported all along and we've been very adamant that these are the issues that are going to move Pennsylvania forward." In addition, philosophical divisions between the House and Senate Republican majorities could prove complicated for Wolf. Those divisions became even clearer in recent days as several major votes showed the House and Senate GOP to be lukewarm, at best, about the other's priorities. For Wolf, at stake is his plan to fix a yawning state budget deficit, narrow funding disparities between poorer and wealthier school districts, ease a massive pension debt and improve the state's economy. It demands more than $4 billion annually in higher taxes, according to an Independent Fiscal Office analysis, and Republicans oppose nearly all of it. The House has heeded Wolf's call to pass a bill to increase state sales and income taxes as a way to reduce the school-funding burden currently shouldered by property taxpayers. Senate leaders are skeptical of it. The House also passed a bill to privatize much of the state-controlled wine and liquor store system, but it has sat untouched in the Senate for three months and, anyway, it is opposed by Wolf and Democratic lawmakers. A significant number of eastern Pennsylvania Republicans might support higher taxes on the natural gas industry, but that influence has yet to be reflected by Republican majority leaders who draw significant support from Pennsylvania's more conservative central and western districts. For his part, many heard frustration in Wolf's letter this week to 17 trade organizations that oppose higher taxes on the natural gas industry. "Why aren't you working with me to fix our schools?" he questioned. Meanwhile, Senate Republicans are smarting over criticism by Wolf's chief of staff, Katie McGinty, that their top priority, a bill to scale back pension benefits, would set themselves up for a "lucrative payout." That attack distorted the facts and disparaged senators, Majority Leader Jake Corman said. Senate Republicans passed the bill and it is now in the House, where noncommittal Republicans are planning to hold hearings on it. Asked about the prospects of two of Wolf's chief priorities -- cutting property taxes and increasing natural gas taxes -- passing the Senate, Corman revealed little. "It's hard to say at this point," said Corman, R-Centre. "They're not making it easy." All that aside, there is no consensus on how to deal with perhaps the state government's most pressing problem -- a projected $2 billion deficit in the fiscal year starting July 1 that has left Pennsylvania's credit rating among the nation's worst. Republicans have yet to unite behind any counterproposal to address the deficit and even the good news -- a $560 million surplus this year through April -- isn't so good. Most of that surplus -- largely from a change in how the state vacuums up unclaimed assets and a jump in corporate income tax revenue -- cannot be counted on to reappear next year, said Eric Kim, a New York-based Fitch Ratings director who follows state finances. "The big revenue over-performance, so far, doesn't indicate for us that the commonwealth's revenue picture is suddenly solved," Kim said. "There's a structural challenge that they need to solve still." ___ Follow Marc Levy on Twitter at www.twitter.com/timelywriter