The lame-duck Congress apparently has killed a Virginia-backed plan to buy 355 acres of land along the Potomac River in Fairfax County, where a proposed housing subdivision is threatening the only nest of bald eagles close to the Nation's Capital.

But local officials said they were encouraged even in defeat, because a House-Senate conference initially agreed to fund the land purchase and only knocked it out Thursday night in a last-minute round of budget cutting.

"I feel very encouraged. I hope we can get it into next year's budget and pray nothing will happen down there" on Mason Neck in the meantime, said Elizabeth Hartwell, vice chairman of the Northern Virginia Regional Park Authority.

Most of the privately owned land, put up for sale last spring and subdivided into 57 housing lots this summer, is surrounded by parkland and the Mason Neck National Wildlife Refuge, the country's first refuge established primarily to help preserve the bald eagle.

The Department of Interior's Fish and Wildlife Service has called the Mason Neck land purchase its No. 1 priority in its northeast region, but has not proposed buying the tract until 1985, because of the Reagan administration freeze on parkland purchases.

Gov. Charles S. Robb, Sen. John W. Warner (R-Va.), Rep. Stanford E. Parris (R-Va.), Fairfax County officials and environmental groups lobbied vigorously to get Congress to authorize the purchase after learning that the major portion of the land -- 296 acres -- was threatened with development. The House approved the purchase but the Senate eliminated it from Interior's fiscal 1983 budget.

This summer, the Northern Virginia park agency leased its 789-acre Mason Neck holdings along the Potomac River to the Fish and Wildlife Service for 60 years to insure the land's preservation as a refuge.

The adjacent national refuge already contains 1,131 acres and Virginia also has a 1,895-acre state park on the peninsula. State and regional parkland completely surround the privately owned 355 acres.

The Northern Virginia park authority proposed to buy the land two years ago but had counted on federal matching funds, which the Reagan administration eliminated.

The federal-state-regional land purchases, of almost half of Mason Neck, came in the late 1960s and 1970s after developers threatened to build a small community on the peninsula that conservationists said would threaten the eagles as well as a major great blue heron rookery with more than 150 nests.

The bald eagle, a national symbol for 200 years and on the endangered species list for several decades, is enjoying a comeback across the country and in the Chesapeake Bay region in particular. The number of eagles dwindled to fewer than 1,000 in the early 1970s, but the federal ban on the pesticide DDT, which weakens birds' egg shells, is credited with increasing the eagle population to almost 5,000 today.

The Chesapeake region had only 20 nesting pairs of bald eagles in 1970 and last year had 93, according to the National Wildlife Federation.

Last winter, 20 eagles spent the cold months on Mason Neck, the largest number in more than 20 years, and a dozen eagles already have arrived this fall to winter beside the Potomac. More are expected as the weather gets colder, according to Jackson Abbott, a retired Army Corps of Engineers official who in 1956 began the annual bald eagle survey in the Chesapeake Bay region at the request of the National Audubon Society.

Abbott called the proposed land purchase crucial not only because it is in the middle of a wildlife refuge but because "the only nesting pair of eagles on Mason Neck have a nest" beside the proposed 296-acre housing subdivision.

The nest is one of a half-dozen, all within less than a mile of each other, that a nesting pair of bald eagles has been using since 1967, Abbott said. " . . . It's not really the same pair since at least one of the mates died" and the surviving bird took a new mate, he said.

Domenick Ciccone, refuge manager, said the eagles have used nests as close as 400 yards to the 296-acre, privately owned tract.

Eagles, which traditionally mate for life, are persnickety birds that insist on nesting privacy and often will abandon nests and even their eggs if disturbed, Abbott said.

While the Mason Neck eagles have produced as many as three eaglets, in the last two years no eggs have survived, apparently because high winds in April of both years severely damaged the nests. Besides the eagles and herons, Ciccone said, the refuge has beavers and this year, for the first time in decades, otters.