Under intense pressure from the County Board, the Arlington school board this week began reviewing ways to make major cuts in the proposed school budget for the coming fiscal year.

Last week, the GOP-majority on the school board directed Acting Superintendent J. Boyd Webb to propose $2 million in cutbacks.

At a work session Tuesday night, Webb presented that list, but emphasized that such "heavy cuts" could not be made without resulting in larger classes and the elimination of at least 35 teaching positions.

Noting that 86 percent of the budget covers employe salaries and benefits, Boyd said, "A lot of the cuts would have to come out of personnel because there's not enough money elsewhere. . . ."

The school board will make the final decision on any cutbacks before forwarding the budget to the County Board, which sets the final figure for school spending.

Webb listed $1.36 million that could be cut from funds covering school personnel and related areas, and $690,328 that would eliminate any program improvements or additional funds for instructional materials and supplies.

Altogether the proposed cuts would affect 57 program areas.

Webb said the major effect would a higher pupil-teacher ratio which could result in a reduction in electives, extracurricular activities and such positions as coaches and teacher aides. The cutbacks also would mean a reduction in supplies and other instructional materials, Webb said.

The proposals brought particularly sharp criticism from the two Democratic-appointed board members, Ann C. Broder and Torrill B. Floyd. Broder and Floyd, who have opposed the plan to consider budget cuts, said the proposal would severely damage the quality of education in Arlington schools.

The cuts were proposed as a result of guidelines issued by the County Board earlier this year limiting the county contribution to the schools to $43.5 million, a 7 percent increase over last year. However, the budget proposed by former Superintendent Larry Cuban called for a $46.9 million county contribution, 15 percent more than last year.The total budget under Cuban's proposal is $59.8 million, or 11.5 percent higher than the current budget of $53.6 million.

At a work session Monday between the County Board and school board, County Board members reaffirmed their intention to seek cuts in school spending.

The proposal to consider $2 million in cutbacks was introduced by school board member Claude M. Hilton at a board meeting last week. His Republican-appointed colleagues, Evelyn Reid Syphax and Chariman O.U. Johansen supported the proposal.

However, Hilton said the cuts should not come from a proposed 10 percent increase in employe's salaries and benefits. The total salary and benefits package is $51.5 million, or 86 percent of the proposed budget. That figure includes teachers' salaries and benefits, $31.1 million, or about 60 percent of the proposed budget.

Two other areas that Hilton said should not be touched are capital improvement funds, $623,000 in the proposed fiscal plan, or building maintenance funds, which total nearly $5.7 million.

Board members Broder and Floyd voted against Hilton's proposal.

The school board hopes to approve a final budget proposal next Thursday and present it to the County Board by March 26.

School board Chairman Johansen warned County Board members at the work session Monday that the budget proposal already may be $500,000 short of what the schools need to operate next year. He added that possible federal cutbacks, proposed by the Reagan administration, could shrink the budget even more.

School officials already are bracing for cuts in federal impact aid and in federal funds for vocational and special education programs. Although school officials have no firm figures on what the cuts could cost Arlington, one official estimated it could be at least $2 million.

Members of both boards noted that additional contingency funds should be included to safeguard against federal cuts.

County Board member Walter L. Frankland said the possible need for extra funds was even more reason that the schools should adhere to the county's spending guidelines.

After the meeting, County Board Chairman Stephen H. Detwiler conceded that additional contingency funds may be needed, adding that "as a practical matter that's the same as funding the regular budget."