A swath of woods that lies beyond the steam and concrete of Washington and past the shopping centers and parking lots of suburban Virginia is at the heart of a little-noticed but intense battle over the Reagan budget.

This is one of the last unfinished portions of the Appalachian Trail, the world's longest continuous wooded footpath, stretching from Georgia to Maine. Here, at a piney patch known as Ashby Gap, hikers are forced to leave the shade and trees of the trail and walk 14 miles on the hot pavement of a commuter highway.

The federal government has spent $1.1 million buying a wooded route along the highway, but no hikers can walk it, at least not until five connecting lots are purchased. Those lots, like hundreds of others bordering national parks around the country, are caught in Interior Secretary James G. Watt's proposed moratorium on park expansion.

Citing a need to curb federal spending, Watt has asked Congress for the second year in a row to appropriate no money for new park purchases, including the remaining 700 parcels along the 2,100-mile trail. "We should seek to become good stewards of the lands and facilities we own before we acquire more," Watt said.

But trail advocates have mounted a strong campaign to persuade Congress to ignore the moratorium and complete the popular trail by 1985, also in the name of fiscal responsibility. Their ranks include all but three of the 28 senators from the 14 states crossed by the trail, officials of trail towns and townships whose economies get a boost from the footpath's estimated 2 million hikers a year and hundreds of trail lovers like 75-year-old Ruth Blackburn, who has fought for the footpath for so long that she jokes of being "married to the Appalachian Trail."

These trail boosters warn that landowners along the footpath are likely to sell property to developers unless the government speeds purchase plans. If second-home developments sprout along the trail, as proposed in some areas including West Virginia and southern Virginia, millions of dollars already invested to protect the natural corridor will have gone to waste, the advocates contend.

An Interior Department advisory commission recently came to the same conclusion, resolving, "Investments already made will be rendered ineffective without the remaining land acquisitions being completed within the next several years."

The trail has been overshadowed by more-celebrated budget battles such as Social Security and defense spending. But its supporters insist their cause is just as important to the nation's future, if in a quieter way.

"What's at stake here is our quality of life," said Blackburn, who chairs the 14,000-member Appalachian Trail Conference, a private group that maintains the trail through volunteer labor.

"We're increasingly losing the ability to get away from the pressures of urban life in this country, especially on the East Coast. We need a place to be quiet, to appreciate the wildlife."

Watt does not disagree, but has strongly opposed spending money to expand the 72-million-acre national park system until its internal needs are addressed. Citing dilapidated roads, sewers and visitor facilities, he asked Congress to increase funding in 1983 for park maintenance, while cutting the land acquisition program to $60 million, enough to cover backlogged condemnation cases and certain pockets of private property within existing parks.

The trail's supporters insist, however, that their cause and Watt's are not mutually exclusive. They portray their request as negligible in the context of the full federal budget.

It would cost $500,000 to complete the 14-mile northern Virginia strip, less than half of what has been spent there already, according to the National Park Service. Finishing the full trail would cost about $28 million, officials said, bringing the total cost to $66 million, or $24 million less than Congress authorized in 1978.

But it is not that simple.

Park advocates in other regions have flagged their pet parks and recreation areas threatened by encroaching development, and are urging Congress to appropriate funds for them, too. For example, poachers are reportedly shooting deer, bear and other wildlife in the Great Smoky Mountains National Park from an area that is within the park's authorized boundary but not yet purchased.

In southern California, the focus is on the unfinished Santa Monica Mountains National Recreation Area, near President Reagan's West Coast home, where real estate prices are rising rapidly. Advocates have warned that the government may soon be priced out of the market.

In Washington state, attention centers on Olympic National Park, where a timber firm recently proposed to cut privately owned woods near the park's popular Lake Ozette. The proposal was rejected, but may resurface in revised form, officials said.

"Everyone has just one item and it's always just a negligible amount in their eyes," said a House Appropriations Committee staffer who has reviewed many of the requests. "Negligible in terms of the whole budget, negligible in terms of the MX missile system. But it's a lot of money in comparison to somebody's Social Security check."

Despite the proposed moratorium, Congress gave about $2.7 million to Interior for Appalachian Trail purchases last year. This year, trail advocates are touting the national personality of the project in hopes of making it a priority again.

Conceived in the early 1900s by forester-philosopher Benton MacKaye as a refuge from "the scramble of everyday life," the trail winds past many of the outstanding natural sites of the East--the Great Smokies of North Carolina and Tennessee, the Shenandoahs of Virginia, the Berkshires of Massachusetts, the Green Mountains of Vermont, the Katahdin of Maine--and is within driving distance of half the population of the United States and Canada.

On a recent visit, the 75-year-old Blackburn strode briskly into the woods outside Paris, ushering a newcomer through the shady realm of pine and maples, mountain laurel and black-eyed Susans, bees and songbirds, until she arrived at a waterfall.

There, cool waters rushed over rocky cliffs and trickled down layers of stone. Sunlight filtered through a canopy of maple trees, reflecting off the water, spotlighting a nearby day lily.

"There!" she exclaimed. "You can't find that on a highway."