As officials of the International Firefighters Union remember it, Jimmy Carter won their endorsement in 1976 by promising to support legislation shortening the work week for 12,000 federal firefighters.

On June 19, 1978, Carter vetoed that very bill, calling it too costly.

In politics, as everyone knows, promises are coin of the realm. If you break them, somebody will get even. On Saturday, in their own small way, the firefighters of Orange County, Fla., got even.

Teamed with retirees of the United Auto Workers, the firefighters turned out 600 to 700 people to vote in the Democratic county caucuses. President Carter's supporters turned out about 500 voters, while the draft-Kennedy forces generated about 300 votes.

The result was a victory for backers of Sen. Edward M. Kennedy (D-Mass.), 17 delegates to 11, and it was especially embarrassing to the president because it came in the Orlando area, where Carter had his headquarters in 1976 and this year.

Unions played a key role in Saturday's caucuses all over Florida. The International Association of Machinists, parts of the locals of the UAW and the Operating Engineers helped Kennedy win Broward County (Fort Lauderdale), for example. The Communications Workers of America, the Seafarers and others helped Carter sweep Duval (Jacksonville), and the Electrical Workers helped Carter in Tallahassee.

But most unions had their own localized mission: to build their own clout at the state Democratic convention in November, where a party platform will be formulated and a presidential straw vote taken.

Orange County was different. Nowhere in the state, it appeared, was there a better example of the intersection of special interest and presidential politics.

"Our international president, William Howard McClennan, had seen assured of Carter's support for the bill personally, by Carter, both before and after he was elected," said Gene Naples, president of the Professional Firefighters of Florida, affiliated with the International Association of Firefighters.

Harold Schaitberger, legislative representative for the international in Washington, said he, too remembered Carter's pledge. "It was at a meeting I attended with Carter and McClennan in Georgia in August 1976," he said. i"I can remember him telling us that he had served as a firefighter aboard a submarine and that he understood the problem."

Carter sent a telegram to the union's convention, which endorsed him later that year. "If I am elected the firefighters will have a true friend in the White House," it said.

The bill in question would have reduced the 72-hour-work week for the 12,000 civilian firefighters at federal establishments to 56 hours. Most other firefighters work a 50-hour week.

Carter vetoed the bill because he said, it would have raised the hourly wage by 28 percent and required the hiring of thousands of new firefighters.

"I don't know the nature of the commitment Carter made to the union," said White House labor adviser Landon Butler. "But I know that's what's bothered them."

"Bothered" is not a strong enough word, union officials say. "We're a special interest," said Naples. "He made a commitment to working people that he did not keep. I recommended to our people in Orange that we go ahead and join" the Kennedy slate of delegates.

On Saturday in Orange County the did.