All three men running for the big job in the government's biggest labor organization have one thing in common: despite the different styles and promises they bring the 300,000 members of the American Federation of Government Employees, everybody after the top union job is running against Jimmy Carter.

Incumbent Kenneth Blaylock is standing on his record of opposition to Carter's federal pay reform, and to moves to cut into retirement benefits. Blaylock predicts Carter will propose a 9.1 percent pay raise this week, more from fear of the bureaucracy than for love of it.

Blaylock's chief opponent of two years ago, Philadelphia regional vice president, Royal Sims, nominated his old foe Tuesday. Sims emphasized that Blaylock isn't one to be pushed or pulled around by anybody. Example: after a recent meeting with Vice President Walter Mondale, Sims told the delegates here (who will elect the next AFGE president) that Mondale asked Blaylock: "Now, how will the AFGE go for president?"

According to Sims, Blaylock looked Mondale in the eye and said: "If the election were held today, I don't know one person who would vote for Carter, and we're trying to find him to hang him." Big laugh from the crowd. Response from Mondale unrecorded.

Carl K. Sadler, who recently resigned as head of the union's political organizing department, promised delegates he will turn the organization around if he is allowed to return to the national office as president.

Sadler, who once directed the AFGE's legislative program, said the union leadership has lost its clout on Capitol Hill and sold out to the administration by backing the controversial Civil Service Reform Act. That law makes it easier to fire federal workers, and sets up a tough merit pay system that has unnerved the 200,000 managers and supervisors whose future pay raises are dependent on it.

Sadler was nominated by AFGE national vice president Alan Kaplan of Chicago. He said a man of Sadler's experience and toughness will be needed next year to deal with President Carter -- or President Reagan -- in matters of pay raises, benefits and retirements. Kaplan said federal workers must be ready to lay their jobs on the line to get a better shake from the White House.

Fred Small, a union leader at the Pentagon, was nominated for the presidency by Norman Fisher of Washington, and Anita Longstreet, coordinator of the 14th District, which includes metro Washington.

Both said that Small is best equipped to run the union to oppose pay "reform" proposals from the White House because of his Defense Department background and the growing threat to federal worker jobs from contracting out.

AFGE is the biggest labor organization in the Washington area. It holds exclusive bargaining rights for 66,000 of the town's 350,000 U.S. workers. Most of the important convention business, dues increases, major constitutional changes and demands from women and minorities for a bigger slice of the union's pie, will be delayed until the balloting begins Wednesday.

Nationally, AFGE has exclusive bargaining right for 600,000 U.S. employes. Like all other federal unions, it lacks the right to bargain over wages or to strike.

About half of the nearly 1,000 delegates here have come instructed to vote for a particular candidate. But enough come with uncommitted proxies from their locals to swing the election to any candidate who can set the convention afire. So far there is lots of smoke, but no fire.