Gov. Tom Wolf arrives at a news conference in December to discuss his rejection of parts of a $30.3 billion state budget plan already a record six months overdue. Now Wolf is defending his budget for next year.

HARRISBURG — Gov. Tom Wolf’s administration began its defense of a $33.3 billion budget proposal Monday, with the Democrat confronting Pennsylvania government’s worst budget gridlock in decades and a Republican-controlled Legislature that is hostile to the election-year tax increase he wants.

Republicans faced off with Wolf’s budget secretary, Randy Albright, at the first Senate Appropriations Committee hearing over Wolf’s warnings of local tax increases and steep school layoffs if lawmakers choose to close a $2 billion-plus projected deficit by spending cuts alone.

“That’s a nice math game, but come on,” Senate Majority Leader Jake Corman, R-Centre.

Corman pointed out Republicans had backed increased aid for schools before Wolf vetoed billions in education aid, and the rate of school property tax increases has slowed in recent years.

Albright responded that Wolf’s warnings are both accurate and realistic, citing the impact of a deep cut in state aid to schools in 2011.

“It’s not rhetoric, it’s math,” Albright responded to Corman.

The December veto by Wolf was at least in part designed to force Republicans to agree to a higher aid figure for schools after a bipartisan agreement supported by Wolf and top Republican lawmakers collapsed in the House.

As a result, billions of dollars for prisons, hospitals, schools and universities remain in limbo.

It was Wolf’s third full or partial veto of a Republican spending plan within six months and Sen. Pat Vance, R-Cumberland, criticized Albright for Wolf’s veto of millions of dollars for hospitals. Hospitals are closing programs and laying off staff, she said.

“For the administration to turn their back on this kind of need, I can’t understand,” Vance said.

School districts also are borrowing to stay open, and Education Secretary Pedro Rivera has said he could not guarantee every school district will be able to stay open, should the stalemate drag on.

Top Republican lawmakers showed no willingness Monday to bow to Wolf’s request for a multibillion-dollar tax increase that has held up passage of a budget for the current year and, Wolf insists, is necessary to underwrite his spending proposal for the fiscal year beginning next July 1.

Sen. Randy Vulakovich, R-Allegheny, expressed frustration over the budget fight, calling it “absolutely pathetic.” But he also suggested he will be less willing to repeat his December vote for a compromise spending plan supported by the governor that requires a tax increase.

“You’re going to have to work a lot harder to get that vote out of me,” Vulakovich told Albright.

All told, Wolf is seeking a two-year spending increase of $4.3 billion, or 14 percent, to $33.3 billion from the last full-year, enacted budget.

Wolf wants the extra spending to close a long-term deficit that has damaged Pennsylvania’s credit rating and to boost aid to public school systems that have among the nation’s biggest funding gaps between wealthy and poor districts. Big increases for pension obligations, human services and prisons are also helping drive the increase.

To pay for it, Wolf wants an 11 percent increase in the state income tax to 3.4 percent, beginning last Jan. 1, plus new taxes on natural gas production, casino gambling and insurance premiums. He also would expand the sales tax to include movie tickets and basic cable television service, and increase taxes on cigarettes by $1 to $2.60 per pack.

The only other state with such budget gridlock is Illinois, where first-term Republican Gov. Bruce Rauner is battling the Legislature’s Democratic majorities.