It’s a guessing game now whether the incoming Republican majorities in the General Assembly will stick to their campaign pledge to close the yawning state budget gap without tax hikes and, if they do, whether Democratic Gov. Bev Perdue will fight them.

In a year-end session with reporters, Perdue didn’t tip her handmuch. But what she said about the critical importance to the North Carolina economy of good public schools, colleges and universities suggested that unless the Republicans bend, she and they are on a collision course for 2011.

For an hour, Perdue frankly discussed the fragile state economy, an estimated $3.7 billion budget shortfall for 2011–12about 17 percent of current spendingand that until state agencies get serious about helping her eliminate all the “unnecessary stuff” there should be no talk of tax increases.

“At this point,” she said, “I don’t know how to spell tax increase. It is off my plate.”

But Perdue also said “there are no absolute lines in the sand,” and she vowed to fight for public education as one of her two “core missions”the one inextricably linked to success of the other, which is economic development and “jobs, jobs, jobs.”

The fact that North Carolina is slipping in education spending compared to other states “doesn’t bode well for us,” she said, especially since the United States as a whole lags behind other nations on measures of student achievement in math, science and critical thinking skills. “It is incumbent on us that North Carolina doesn’t fall behind,” she said. “It won’t happen on my watch.”

A report, “Race to the Bottom,” issued in October by the Public School Forum of N.C., a Raleigh think tank, said that budget cuts in 2008–09, at the outset of the Great Recession, pushed North Carolina down to 42nd of the 50 states on per student spending in grades K–12. If lawmakers try to balance next year’s budget with spending cuts alone, the report warned, North Carolina could find itself 49th, or even last.

Perdue hosted a dozen reporters at the Governor’s Mansion, the first floor of which is beautifully decorated and open to the public for the holidays. As the hour was ending, First Gentleman Bob Eaves descended from the upstairs living quarters to show off their two shaggy dogs, Tibetan terriers named Dosie and Zipper. The relaxed yet serious mood was consistent with Perdue’s comment that, though she wasn’t predicting how next year’s budget struggle will turn out, “I know where we’re headed.”

The depth of the budget hole ahead was set out last week by the N.C. Budget & Tax Center, an arm of the N.C. Justice Center. For 2011–12, the state will need $21.9 billion in revenue just to maintain current services, it said, including state aid to counties and cities. Of the total, $11.9 billion is for education, including $8 billion for K–12 schools.

But estimated revenues for next year, the center reported, are just $18.2 billion. One reason for the shortfall is that federal stimulus funding will end after two years. Another is that temporary tax hikes enacted in 2008 with Perdue’s support, a surtax on upper-income taxpayers and a 1 cent sales tax hike, are also ending.

The tax hikes generate almost $1.4 billion a year. Perdue has said she won’t ask the General Assembly to extend them when she sends up a draft budget next year. That doesn’t mean they won’t be needed, however.

Perdue ordered agency heads to submit budgets with 10 percent cuts to education programs and 15 percent to all other state programs. But even such worst-case budget scenarios would still leave $1.1 billion to be made up by bigger cuts or tax increases.

Perdue began by saying that she’s comfortable playing the bad fiscal cards the economy’s dealt her, however much she might’ve preferred being governor in good times. Instead, her two years in office have been the worst for North Carolina since the Great Depression, forcing her to drastically slash the budget, to enact unprecedented furloughs of teachers and state employees and to raise taxes. “I’ve made the tough calls,” she said.

Looking ahead, Perdue said she has no choice but to continue cutting given the weak recovery of the national economy. In that task, she’s listening to every idea she hears, whether from Republicans or Democrats, state officials or local leaders.

What she won’t do, she said, is to chip away at programs to save money in the short run, knowing these cutbacks will result in higher long-term costs. Whittling away at some home-health services, for example, could push indigent clients into state-subsidized nursing homes.

Perdue also said she’ll oppose reshuffling school aidan idea popular in Republican circlesif doing so penalizes poor children. “If the [local school] systems can save $1 billion with flexibility, Katie bar the door, give them flexibility,” she responded. “But remember, the constitution requires that [they] give every child a free and equal public education.”

Without repeating them, she cited her previous comments regarding “the situation in some of our counties”a reference to her past criticisms of the trend toward unequal, racially divided schools in Charlotte-Mecklenburg, New Hanover and Wake counties.

In effect, she’s challenging the Republicans to show her how state spending can be slashed without cutting vital services. “It’s easy to talk about [cutting budgets] when you’re running for office,” she said. “It’s hard to do when real lives are at stake.”