Once the leaders of the pack in the rush to distribute emergency federal funds for construction-related jobs, the General Services Administration now appears to be running like an old, lame mare ready for the glue factory.

GSA officials say the calendar may now show fiscal 1984 before it is able to award any of the emergency-jobs money that Congress authorized last March. Other agencies contacted, including the Veterans Administration, the Department of Commerce and the Army Corps of Engineers, that had a share of the $1.4 billion in construction-related funding is ahead of GSA in the planning process.

This is an abrupt turn-around from the days immediately before the legislation became law. At that time, Public Buildings Commissioner Richard O. Haase confidently projected that advance planning would put the agency at the forefront of the effort to distribute its $125 million share of the money to regional offices.

Staff cutbacks and confusing rules for the special funding apparently played a part in bringing the distribution process to a virtual halt in May. Haase was forced to call a conference in San Francisco to sort out the mess.

"We are behind," admitted Haase this week. "But the planning is over and the seed money for design work--some $7.5 million--is now in the hands of regional officials."

Walter E. Huber, a project operations director for GSA's National Capital Region, said his office is so short-staffed that "we can barely get done what we were supposed to before the jobs bill passed. It's unlikely we'll start a single project in fiscal 1983 as a result of the jobs-bill money."

The D.C. regional office got $510,000 for planning work leading to contracts, and it has asked for $26.94 million of the $125 million pot. Haase, however, said the funds would be distributed nationwide on first-come, first-served basis so the money can be moved to contractors quickly. The only caveat, which is contained in the law itself, is that 75 percent of the money must be spent in what is known as labor-surplus areas.

Construction projects in the $4.65 billion jobs bill ranged from $179.6 million for family housing units on military bases to $25 million to speed the repair of deteriorated National Park facilities, and from $60 million for federal prison construction to $50 million to weatherize schools and hospitals.

The delay by GSA, however, doesn't mean that its projects will begin much later than those of other agencies. At the Economic Development Administration, $100 million for needy community development projects will be apportioned quickly on paper, but the checks won't be awarded until September. EDA merits special mention because the Reagan administration tried to scuttle the agency itself this year. As a result, EDA so far has delayed spending all but $16 million of its $198.5 million funding. When the agency got the additional $100 million, its staff was already up to its ears in applications for the money.

Footnote: The administration is trying to reclaim a sizable portion of the construction funds by submitting reductions to the budget. There's some irony to that: If it turns out that most of the money in the emergency appropriations is not actually "spent" until after October 1, then there really was no need for the emergency bill.

At the urging of members of the New York congressional delegation and Interior Secretary James G. Watt, GSA Administrator Gerald P. Carmen has agreed to review his decision to try to negotiate the sale of a valuable New York City park property. The delegation and Watt want the 32-acre parcel turned over to the city, free of charge, for use as a park. GSA awarded the city 11 acres of adjacent park land at the old military installation known as Fort Totten, but it sought a negotiated sale for the remaining acreage. Dale F. Hawkins, GSA's eastern states property sales director, said "we've agreed to the review, but we still plan to send a letter to the city that asks them to begin negotiations."