Metrorail finally has a construction budget for fiscal 1982, after months of lobbying in congressional offices and fretting at board meetings. Just over $284 million in federal funds will allow completion of most of the first year of the building program the Metro board approved last August.

That level of federal funding got final clearance this week when President Reagan signed the 1982 appropriations bill for the Department of Transportation. About $50 million in state and local funds will be added to it.

Metro's plan originally had assumed the federal government would provide $315 million this year, a sum the House had approved before receiving demands from the White House for further cuts. The Metro board must now consider ways to reduce this year's spending by $31 million.

The Metro staff has proposed dropping a $15 million contract to begin tunneling for the planned U Street station of the largely unbuilt "inner-city" Green/Yellow Line and cutting out real estate purchases for the Yellow Line spur to Franconia-Springfield in Virginia and for Green/Yellow Line segments to Greenbelt.

These changes would push back by a year or more the increasingly distant and uncertain completion dates of the unstarted segments of the Yellow and Green lines. Those segments are targeted for completion in the late 1980s and early 1990s.

The construction agreement signed in August came after months of negotiation among Metro's eight member jurisdictions. It provides that if federal funding falls short of expected levels, as it now has, cuts will be distributed on a pro rata basis among member jurisdictions, as the staff proposal attempts to do.

The agreement reflected grave concern of Prince George's County and District officials that for every year that the Green and Yellow segments remain unstarted, chances increase that they will never be built at all.

By concentrating the cuts in those two lines -- Metro officials say there is no other logical place to put them -- other opening schedules might not be disturbed: Yellow Line track between Gallery Place and the Pentagon and Blue Line track south from National Airport and Huntington would still be able to open late in 1982 (though that deadline is in doubt).

The Red Line, meanwhile, would be extended through to Shady Grove in late 1983 and the Orange Line to Vienna in 1986.

Metrorail relies on federal grants for about 85 percent of its building costs. Concern increased earlier this year after the Reagan administration took office and announced it would commit itself only to funding completion of 75 miles of track for the time being, not the master plan's full 101 miles.

With the 1982 budget struggle completed, Metro officials are now turning their attention to fiscal 1983, where obstructions are already threatening the $375 million that Metro wants from the federal government.

Federal officials had tentatively approved that sum, on the condition that it was composed of $100 million from funds cleared by a special Metro construction bill, known as Stark-Harris, and $275 million from "interstate transfers," in which funds for canceled interstate highways are traded in for a like sum for Metro.

Since the canceled roads were to be in the District, its permission is needed to give the money to Metro. However, the District has long been on record as wanting to use much of the $275 million in transfers to rebuild two city bridges and resurface 35 miles of highway annually.

Under this scheme, Metro would get only $155 million of the $375 million in federal funds needed for the second year of the approved four-year construction program. "At 155 we don't have a program," said one Metro official, since that figure would cover only past overruns, insurance, consulting projects, rail car purchases and other non-construction costs.

However, a year of negotiation remains before the 1983 appropriations bills come up, and Metro officials point out that much can happen in that time. One idea is to persuade the District to take less for its roads projects.

For the present, though, the District remains adamant that it wants the bulk of the money for the long overdue repairs. "We will have put in over $2 billion in interstate transfer money into Metrorail construction" by then, said D.C. Transportation Department Director Tom Downs. ". . . We're not going to be painted into the corner on the issue."

Another proposal is to take more than the $100 million from the Stark-Harris funds. Enacted two years ago, the bill cleared the way for $1.7 billion more in capital funds for Metro. However, the Reagan administration is reluctant to spend more than $100 million from it next year so as to hold down the overall level of the federal spending.