Just south of Leesburg, an elegant Southern courthouse town 40 miles up the Potomac from Washington, is a one-runway municipal airport built mostly with federal funds.

To the east of the Loudoun County seat is a sewage treatment plant, the key to the town's future growth, that is now being modernized and enlarged. Washington is paying for most of the renovation -- $250,000 this year alone.

Around the old freight station at the center of this town of 8,500, a redevelopment program aims at rejuvenating a neighborhood that has slowly declined since the Washington & Old Dominion Railroad stopped running in 1968. Leesburg is counting on the federal government to pay the $1.3 million bill for that project, too.

In all, nearly one dollar in six of Leesburg's $6.5 million budget comes from Washington. Yet town officials seem little troubled by the $35 billion in federal budget cuts that begin to take effect today.

Two days ago, in fact, Leesburg Mayor Kenneth Rollins drove to the White House to have his picture taken with the president. Rollins wants to use the photos to boost his Republican campaign for the Virginia legislature, and few doubt that Reagan's support remains a political asset in Leesburg.

"We deal mostly in hard goods," Town Manager John Niccolls said, referring to streets and sewers and storm drains. "The cuts are mostly in social services."

Leesburg's poor residents -- largely hidden by the town's $27,000 median family income and by Loudoun's horse-country image -- will be affected by the cuts. About 260 Loudoun families receive Aid to Dependent Children, and many of them live in Leesburg, which has Loudoun's only subsidized housing.

The poor depend on the county government, not the town, for help. "It's such a stressful time to work here, because we just have nothing to offer," said social worker Kiran Starosta yesterday from behind the wheel of a rattling county car. Starosta was on her way to visit Mary Green, who had called the day before for help that county officials are not sure they will be able to provide.

Green's mother, who worked for 40 years taking care of the house and children of a Leesburg family, now needs constant care herself, Green told Starosta. Her 76-year-old mother recently underwent kidney surgery; she needs to be driven three times each week for dialysis treatment at Fairfax Hospital; she must follow a strict diet, but she cannot read.

Green quit her own job last week to prepare for her mother's return from the hospital, but the two women cannot both live on the mother's $290 monthly Social Security check, Green said. And county officials agreed: Green probably deserves some financial support or the help of a companion service that would allow her to return to work.

But Loudoun is losing $93,000 of the $566,000 in federal and state funds that went into social services last year, and programs such as the ones Green needs were among the first to go. There is no money for Mary Green, according to Loudoun social services director Joan B. Linhardt, and if Green gets help, someone else may not.

County officials are still sorting out the effects of the cuts. The first welfare checks affected by the cuts will not go out until Nov. 1. The lease of the imperiled county legal aid office does not have to be canceled or renewed until Jan. 1.

Officials said they had some idea of the impact until Reagan went on television last week to ask for still more cuts. What they expect:

About one-third of the 660 Loudoun residents on welfare, or Aid to Dependent Children, will see their benefits reduced, according to eligibility supervisor Ron Eamich. About 40 families -- those with a working parent especially -- will be knocked from the rolls entirely.

Within a few months, Eamich said, many of those working parents will have given up their jobs and will be back on welfare, qualifying for more aid than they now receive. Working mothers on welfare now receive only $10 or $20 as a supplement, and Eamich said they could stand to lose that; but if they are ruled ineligible for welfare, they and their children will also lose Medicaid, which covers their doctor and hospital bills.

Attorney Gerard S. Rugel said his Leesburg office will probably be the first legal aid center in Northern Virginia to close when the cuts take effect. Rugel helped about 100 people in the last few months, most of whom had run into trouble with welfare and disability workers or with their landlords. "Some of them are going to be literally on the street with no place to go," Rugel said yesterday.

The county's information and referral service will shut down Oct. 9. Although the service's two workers have worked on almost every imaginable problem -- they once matched one Loudoun resident with a pet lion with another resident who had found a dead deer in her yard -- they mostly functioned as an advocacy office for poor and elderly residents who could not fight their way through various government bureaucracies.

"Those people will be left with nowhere to go," said referral worker Ruth Gerbec, who hopes to be eased into a vacancy somewhere else in the county. "It's sad."

Leesburg itself is in good fiscal shape. The town is receiving $100,000 in revenue sharing funds this year for its police department; $150,000 to develop a park near the subsidized apartment building, Loudoun House; $450,000 for the redevelopment project around the train station; $225,000 for the sewage treatment plant; and $40,000 for the airport -- all told, about $975,000 in a budget of $6.5 million.