Although their budget deliberations for fiscal 1983 have not formally begun, Arlington County officials received grim news last week: If the tax rate remains the same, the county may face a deficit of $4.7 million or more in the next fiscal year.

The projected deficit is based on a maximum 5 percent across-the-board increase in county spending suggested several months ago by County Board member Walter L. Frankland.

But the deficit, county officials say, could go as high as $7 million if teachers and other school employes receive the same 5 percent pay raise that has been suggested for county employes.

The projections came at an informal and controversial meeting of County Board Chairman Stephen H. Detwiler, County Board member Ellen M. Bozman and two school board members. The meeting was called to "set the tone for the budget processes" for the coming year, according to Detwiler.

And while Detwiler and Bozman both said it is too early to predict, they indicated the board could be forced to increase the tax rate for county homeowners to bridge the revenue gap. The current rate is 96 cents for each $100 of assessed value.

The main topic at last week's session was a "guideline for spending" the County Board is expected to set for county schools this Saturday.

Last year, the board set a guideline allowing no more than a 7 percent increase in county contributions to the school budget, while the school board submitted a fiscal plan that was more than twice that figure, or 15 percent. In the end, after a particularly divisive battle on the school board and some sharp exchanges with County Board members, the schools got $44.7 million from the county, or an 11 percent increase. That figure allowed for a 6 percent pay increase for school workers.

Despite the efforts of School Board Chairman Claude M. Hilton to head off the bitterness of last year's budget battle, there already are signs of an impending conflict, particularly if the County Board adopts the maximum 5 percent spending increase suggested by Frankland.

"I anticipate the guideline you give us would be a realistic one, although not one locked in concrete," Hilton told Detwiler and Bozman at their meeting last week. Hilton, along with school board member Simone J. (Sim) Pace, represented the schools at last week's session.

School officials already have questioned the ability of the schools to operate under a 5 percent spending limit, which, according to county staff figures, would mean a $47 million contribution from the county, or about $2 million more than last year.

School Superintendent Charles E. Nunley noted, however, that the schools need at least 4.5 percent more money than last year "to sustain what we have now." That increase, Nunley said at the session last week, would cover only mandatory increases in expenses such as Social Security, insurance premiums, retirement-fund contributions and step increases in salaries.

Increased costs for fuel and for discretionary items, such as new books and funds for the substitute teachers' account, which Nunley said is currently underbudgeted, would bring school needs even higher -- to about $2.8 million more than the $47 million figure, Nunley said.

Even then, Nunley and Hilton said, that doesn't take into account pay increases for teachers -- which would cost about $473,247 for each 1 percent of any raise -- or losses from reductions in federal aid to school programs.

Detwiler warned, however, that this could be the toughest budget year yet for the county.

"This will be the tightest and probably the most difficult budget I've ever worked with," Detwiler predicted. "But if you hold to the assumptions (in the staff budget analysis), there's only one source of revenue we can look to. I would hope (there is no tax increase), but I'm certainly not optimistic we can approach the kinds of (budget) reductions we've made in the past."

The informal session drew sharp criticism from other school board members, who complained that the meeting was called without consulting the full board.

Detwiler, who originally proposed the meeting, said he had wanted both the full County Board and the school board to attend, but because of scheduling conflicts he eventually suggested to School Board Chairman Hilton that only two members from each body attend. The session was opened to the public after a complaint from the media, Detwiler said. (Virginia law requires all county and school board meetings to be open to the public if three or more members from either body are participating. The major exceptions involve discussions of personnel, legal and certain real estate matters.)

School Board Vice Chairman Evelyn Reid Syphax and board member Torill B. Floyd said they had no objection to the four-member format but were angry because they learned of the session barely 36 hours before it began at 8 a.m. last Friday. Syphax and Floyd both attended as members of the audience, not as official school representatives.

"The issue was I didn't know about (the session)," Syphax said. "I felt the vice chairman should have known about it prior to the announcement as a courtesy to the vice chairman. . . . We had not had any board discussion (on the budget items) and we should all be knowledgable about board matters."

School board member Floyd added, "The way it was handled really worries me. We had never had (the budget material) on the agenda so (Hilton) didn't have any guidance from the school board before he went to the meeting.

"And the problem is, they got pretty close to setting the budget guidelines (at the session) without the rest of the school board members" participating.

Hilton, however, said all school board members had been given the full budget information before a school meeting early this month, and that he and Nunley were simply going over the information with Detwiler and Bozman.

"The information was sent to all the school board members . . .," Hilton said.

Despite her complaints, Syphax said she was generally pleased with the tone of the meeting. "I didn't know what they were going to say," Syphax said, "but I'm especially pleased with (Hilton's) comments (on spending guidelines)."