Arlington County is facing its largest tax revenue shortfall in almost a decade, a situation that could force the County Board to cut back programs and staff in next year's budget, officials said yesterday.

A slumping real estate market, falling tax collections and federal budget reductions have left the county with a projected $6.7 million shortfall in its 1984 budget, County Manager Larry J. Brown told the board at its regular meeting.

Brown said the county needs a 5 percent budget increase to meet increasing costs caused by inflation and to raise county employes' salaries 3 to 5 percent.

"Every year we have the gloom and doom forecast," said GOP board member Dorothy T. Grotos. "This year the gloom and doom is a little deeper than they usually put on."

The slumping economy prompted county officials to begin their budget process early this year, though the board will not vote on a budget until next spring. The county manager has recomended a $174.2 million budget for next year, a 5 percent increase from this year's budget.

Brown has recommended maintaining the current real estate tax rate of 98 cents per $100 for the 1984 budget, although this year's realty tax collection is now projected to be about $3.8 million less than originally expected.