Sgt. Richard Beebe was packing the family car outside his small brick duplex at Fort Belvoir, where he lives with his wife and daughter.

He was going on a fishing trip, and Beebe says it may be the last he can afford if he has to pay tuition for his daughter to attend Fairfax County public schools -- a move the county is threatening if it loses nearly $6.9 million in federal impact aid it expects to receive next fall.

Beebe's daughter Lynel is a fifth grader at Markham Elementary School, one of three Fairfax County public elementary schools on the post.

If Fairfax charges tuition to Fort Belvoir parents, Beebe, who makes $13,000 a year as an Army sergeant, would have to pay at least $2,800 a year to keep Lynel in school.

"Financially, forget it," he said, half-laughing at the idea of paying for a free public education. "I'd have to work two jobs, plus my wife would have to work. Either that or give up everything, do nothing.

"That's like asking tuition for private school. I think it's kind of silly. If anything, the government ought to pay for us if there is a tuition, especially if we live on post."

Officials at Fort Belvoir are holding their breaths until the congressional dispute over impact aid is resolved. But they say they can sympathize with military families, especially enlisted personnel, who are wondering how they could afford the tuition tabs, which Fairfax officials have estimated could cost from $2,800 to nearly $10,000 for severely handicapped students.

"We're talking about a lot of individuals who make maybe $9,000 to $10,000 a year," said Maj. David E. O'Donnell, Fort Belvoir's liaison officer with the school system. "If that's all you're making, how can you come up with $3,000 in tuition? A soldier coming here didn't expect to have to pay $2,800 in tuition, not that he had any choice in coming to Fort Belvoir."

O'Donnell said that roughly 1,350 enlisted families and 500 officer families live at Fort Belvoir. His major task at the moment, he said, is monitoring developments and keeping the post informed.

Approximately 1,520 students whose parents live at Fort Belvoir attend Fairfax County schools. About 1,000 attend the three on-post schools, and about 500, in grades seven through 12, attend Hayfield Intermediate-High School, which is off-base. Since the federally owned fort is not taxable and since non-Virginia residents who live on post do not pay local taxes, the county is compensated with "impact aid" to help offset the costs of providing a free education to the 1,520 students.

Impace aid comes in two categories: "A" for those districts serving children whose parents both live and work on federal property, such as military personnel living on-post; "B" for districts serving children from federal housing projects or whose parents live on private property but work on federal property, such as a Labor Department employee who owns a home in Fairfax -- and pays local property taxes -- but works at a federal building in the District.

The Reagan administration wants to eliminate all "B" funds and limit "A" funds to districts where 20 percent of the students live on federal property. Currently, a House proposal would kill the entire impact aid program, while a Senate proposal would retain $200 million, limiting it to pay for children of military personnel who live and work on military bases. The proposals are not expected to reach the floor of either chamber until next week at the earliest.

In Fairfax County, about 18 percent of the 124,870 students fall under one of the two aid catagories, according to budget official Joe Romeo. Of those, only 1.2 percent come under catagory A.

Arlington County, which could lose up to $929,000 in impact aid, has about 240 category A students from Fort Myer, or about 1.6 percent of the total 15,146 enrollment. Alexandria, which could lose $450,000 to aid, has no category A students, according to school officials.

This winter, in preparation for the long-threatened loss of impact aid, the Virginia General Assembly authorized localities to charge military families tuition if impact aid fell belor 50 percent of total per capita costs of educating those students. Only on-post families would be affected, and Virginia residents, even those who live on post, would be exempt.

So far, Fairfax County is the only Northern Virginia jurisdiction to exercise the tuition option.

It did so by notifying federal and military officials that it "regretfully" intended to charge tuition to affected students, or to close the three on-base schools. Fairfax officials urged the Defense Department to sit down with them and work out a plan for the department to run the on-base schools or to pick up the tuition bulls so the financial burden would not fall on already strapped military families.

While Congress attempts to come up with a final plan, and while local school districts continue their threats of tuition charges, the Defense Department itself is considering challenging the constitutionality of charging any military family for a public education.

But, in the meantime, it's hurry-up-and-wait at military installations like Fort Belvoir. An Army spokesman said post commanders have been notified to alert soldiers receiving tuition bills to forward them to a designated officer and "not attempt to personally resolve matters regarding tuition fees with school authorities."

Many military officials hope the matter will be resolved soon.

"Fairfax County has a reputation for excellent schools," said liaison officer O'Donnell. "It's important to us. We're part of this community and it's important to maintain a very good relationship with them. Children and parents like the school system here. . .

"They've said (school closings and tuition fees) are last resort options. I think the county is trying to resolve this situation is a matter that will meet their requirements and impact the least on the individual soldiers."

But for many military families, just the threat of a tuition bill makes them angry.

"It's just like saying, 'Why don't you send them to private schools?' because that's how much it would cost," said Kathy Higgins, a Hayfield High School junior who was shopping with her mother at the post commissary.

"If they close these schools, look at the number of civilians they'll put out of work," added her mother Marianne. "And a lot of people here work off the post and do the bulk of their shopping off the post. So they're still paying taxes to the county."

Tom and Sue Stater, who live on-post, have two children, including a 6-year-old in Fairfax schools, and are expecting a third child. Slater said he earns about $11,000 a year as an E-6 and finds the prospect of tuition "rather scary."