Northern Virginia schools will lose $3.1 million in state aid next year if Gov. Charles S. Robb succeeds in selling his package of controversial budget cuts to the General Assembly.

Robb's proposal to cut $20 million in school aid already has generated opposition both inside and outside the legislature, even though many noted that the cuts -- coming after last year's increases in the education budget -- were relatively small.

Fairfax County, which operates the largest school system in the state, would absorb the brunt of the cuts -- $1.7 million -- and school officials there say it would create serious problems for the county's recently proposed $450 million school budget.

"It hurts," said Fairfax Superintendent William J. Burkholder. "The budget we developed provided for only 5.1 percent overall increase. It was a very tight budget and now we have to go through it all again."

The reaction from teachers -- who Robb last year promised would receive 10 percent pay raises two years in a row and now face a 6.3 percent increase this year -- was even stronger. "We are very upset," said Marilyn Rogers of the Fairfax Education Association. "Robb ran on a platform of commitment to education and we look at this as a major step backward on that commitment."

Some legislators predicted that the cuts will be modified before Robb's amended budget clears the assembly. "It is almost impossible to avoid any cuts in public education, but I would hope we could lessen it," said Del. Dorothy S. McDiarmid (D-Fairfax), chairman of the House Education Committee.

And while no one was happy about the cuts, some said it could have been worse. "It's not as though we didn't expect it," said Virginia Education Association lobbyist Dick Pulley. "What we were fearing was something that could have been much greater."

Del. David G. Brickley (D-Prince William) said he hopes to mount a Northern Virginia effort to stave off education cuts by allowing localities to double the state's tobacco tax, now at 2.5 cents a pack. "We could use it as a bargaining chip," Brickley said.

Robb came in for other criticism on his budget cuts, designed to shore up a projected $175 million revenue shortfall this year. State employes were angered by his proposal to freeze their salaries, a move expected to save $35.8 million by denying step increases to the workers.

Some legislators were even more upset about $9.2 million slashed from mental health, an area exempt from the governor's first round of cuts, but which is now likely to translate into reduced funding for local drug and alcohol rehabilitation programs.

In Northern Virginia, for example, community agencies recently received promise of a special state grant of $418,981 to operate drug clinics, halfway houses, and detoxification centers in Arlington, Alexandria and Fairfax. How much that would be reduced will remain uncertain until Robb's proposed cuts are translated into county-by-county figures, but some legislators said they wanted the funds retained. "I think it's more important that we address stuff like that before we restore one percent in education," said Del. L. Cleaves Manning (D-Portsmouth), the chairman of the Counties, Cities and Towns Committee.

Local officials were scrambling to calculate the impact of other cuts in local grants and aid programs. "Local governments are coming off a three-year cycle of tight budgets and any cuts, state or federal, are going to have some impact on services," a spokesman for the Virginia Municipal League predicted.

Overall, state agencies and departments, including higher education, have been asked to shoulder most of the burden of the projected deficit of $305 million in the state's 1982-1984 budget. The shortfall already has been reduced by a series of budget-cutting moves ordered by Robb.

Selected agencies -- with aid to education and local governments exempted -- were required to cut back spending by 5 percent last spring. Construction projects totaling $32 million were delayed. And now, state agencies are being asked to cut spending by 6 percent next year, for a total savings of $62 million.

In a move that will save the state $53 million in a one-shot savings, Robb ordered a freeze on all school construction projects financed through the state Literary Fund. That fund, created in 1869 from court fees and fines, has been lending up to $2 million per project at 3 percent interest since 1954.