Baked beans and potato salad sat untouched in silver bowls; hamburgers and hot dogs were piled uncooked by the grills. The White House chefs, for once, could almost relax.

The leftovers even extended to the boxes and boxes of presidential pins, pens and cufflinks handed out as prizes for the obstacle course, the egg roll and the sack race.

It was Jimmy Carter's first Labor Day picnic for the nation's union leaders last night, what some saw as an effort through socializing to patch up steadily deteriorating relations with labor. He and Rosalynn Carter had flown up from Georgia to host it and a number of their guests had flown in from around the country to be there.

The turnout, though, was well below what White House organizers had expected. When invitations were mailed 10 days earlier, the staff was prepared for 1,600. Early yesterday, they were anticipating 1,200. Last night, 870 labor leaders, members of Congress and some of their families showed up.

But it appeared to be a supportive crowd.

"Tonight I saw him build some bridges and demonstrate an understanding for the legitimate role labor plays," said Bob Dunleavy, assistant to the president of the International Brotherhood of Electrical Workers. "I thought his speech was a little conciliatory to labor, and I was favorably impressed with it."

The speech, incidentally, also included a reference to the aquatic, long-eared beast that allegedly attacked Carter while he was fishing near Plains.

"Rosalynn and I cam back from Georgia," Carter told the crowd. "We escaped from all the killer rabbits down there."

That drew a laugh from the crowd, which included Hamilton Jordan, who wore a coat and tie to keep up his new chief-of-staff image. Jordan had some comments of his own on the beast.

"I believe in killer rabbits -- and killer reporters," he said. "But a killer rabbit has never come after me and a killer reporter has."

Last night, reporters watched Jordan as he talked to several young women during the president's speech. When some of them asked him about the charge he snorted cocaine at Studio 54 in New York, he responded: "But I didn't do anything . . . aaaaah, don't write that down -- I'm not supposed to talk about it."

Others from Carter's White House staff mingling with the crowd were aides Sarah Weddington, Richard Harden and Frank Moore, who ran the obstacle course against Redskin center Ted Fritsch. Moore lost.

A dozen Redskins and their wives supervised the games which a number of the labor leaders played -- and survived. Last week one unionist had said that "you could alter half the membership of the AFL-CIO executive council with one energetic volleyball game."

Redskins linebacker Pete Wysocki easily managed the obstacle course, although he lost to his wife Sylva. And even as Wysocki happily attacked one of the 1,920 hamburgers served at the picnic, he refused to be wooed.

"Hey, I can't be bought by a hamburger," he said. "I'm apolitical."

There was nothing apolitical about the rest of the crowd. Some, in fact, had hoped Carter might use the occasion as a kickoff for his reelection campaign.

"This could have been the real prelude to the 1980 campaign," said a labor leader from the South. "Instead we got the same old malarkey."

Carter departed from his prepared speech to touch upon energy, peace, Salt II and a national health program. He also made references to "George Meany, my friend," who didn't attend because he had a virus.

"Meany," Carter said, describing a phone conversation he'd had a few minutes earlier with the 85-year-old president of the AFL-CIO, "is a fine man. He was kind of reading me my report card on the telephone. He said if I wouldn't tell what was on it he wouldn't."

The president continued with the joke.

"There are three things a president always has on his mind. National Security -- that's always present. Congress, always present. President George Meany -- that's the third."

"I think the president made points with everyone," said Rep. Charles Vanick (D-Ohio). "Whether it works with labor, we'll have to wait a few months to see."

"I think this is a nice lighthearted touch," Rep. Edward J. Derwinski (R-Ill.) said. "We don't have enough of these things in Washington."

The Newspaper Guild's Charles A. Perlik Jr. called the speech "low key," its tone "good" and the evening "a helluva party."

"Most of these people, including myself, were at the Labor Day dinner here nine years ago with Richard Nixon," said Perlik. "If we could go to a Labor Day dinner with Nixon, we can sure go to a picnic with Carter."

Another labor leader, asking not to be identified, said his union colleagues were giving Carter until Thanksgiving "to turn it around -- he just doesn't understand the labor movement, the working people or their problems and aspirations."

The Carters shared the open-air stage with Labor Secretary and Mrs. Ray Marshall. Scattered among the audience from Capital Hill were Sens. Claiborne Pell (D-R.I.) and Jacob Javits (R-N.Y.), Reps. James Corman (D-Calif.), William Brodhead (D-Mich.) and Charles B. Rangel (D-N.Y.). From labor came Lane Kirkland, secretary-treasurer of the AFL-CIO executive council, along with representatives of major U.S. unions.

Not on the acceptances list released by the White House, however, were Teamsters president Frank Fitzsimmons, United Auto Workers president Doug Fraser, United Farm Workers president Cesar Chavez, American Federation of State, County and Municipal Employes president Jerry Wurf and International Association of Machinists president William Winpisinger. Most, however, sent representatives.

Even the Musicians' Union was represented.

"It's really kind of neat, you know," said Stephen Wade of Chicago, the banjo player who provided the entertainment.

And did he support Carter for reelection?

"I had a lovely time here tonight," he said, adding, "and that's all I mean to say."

A partial list of guests at last night's Labour Day picnic at the White House: AFL-CIO EXECUTIVE COUNCIL Lane Kirland, secretary-treasurer Emmet Andrews, president American Postal Workers Union Kenneth Blaylock, president American Federation of Government Employees Charles Pillard, president International Brotherhood of Electrical Workers Glenn Watts, president Communications Workers of America OTHER INTERNATIONAL UNION PRESIDENTS Willard McGuire, president National Education Association Edward J. Carlough, president Sheet Metal Workers International Association Kenneth Brown, president Graphic Arts International Union Joseph Pollack, president Insurance Workers International Union Joseph T. Power, president Operative Plasterers and Cement Masons D. J. Beckstead, president United Telegraph Workers Charles Brodeur, president International Union of Wood, Wire and Metal Workers Pascal DiJames, president Tile, Marble, Terrazzo, Shopmen and Finishers International Edward J. Kiernan, president International Union of Police Association William A. Gill Jr., president Flight Engineer's International Association Angelo Lo Vacchio, president International Plate Printers, Die Stampers and Engravers Valentine Murphy, president Utility Workers Union of America AFL-CIO DEPARTMENTS Robert Georgine, president Building and Construction Trades Department Rudy Oswald, director Research Department Al Zack, director Public Relations Department Ken Young, director Legislative Department Al Barkan, director Committee on Political Education Paul Burnsky, president Metal Trades Department Jacob Clayman, president and secretary-treasurer Industrial Union Department Jean Ingrao, secretary-treasurer Maritime Trades Department Bob Harbrant, secretary-treasurer Food and Beverage Trades Department OTHERS Tom Donahue, executive assistant to president Stephen Schlossberg, director of Government and Public Affairs, United Auto Workers Elizabeth Koontz, co-vice Chair President's Advisory Committee for Women; chair, National Commission on Working Women STATE PRESIDENTS AFL-CIO William Cleary, Massachusetts Robert Oleson, Illinois Herb Mabry, Georgia James Mahoney, executive vice president Pennsylvania