The White House got its "Labor-forCarter/Mondale" bandwagon rolling yesterday with six passengers and lots of seats left for late-comers.

Gingerly sidestepping questions about a possible presidential bid by Sen. Edward M. Kennedy (D-Mass.) officers of six major unions representing about 3 million workers held a new conference at the Hay Adams hotels to endorse President Carter for reelection next year.

They said they were making the early endorsement because Carter is in trouble and needs their help.

Their unions -- centered in the garment, railroad, communications, retail sales and maritime industries represent six of the 105 AFL-CIO affiliates and about 15 percent of all union members in the country.

They acknowledged that a number of union leaders had refused to join the group now but predicted they would do soon. Representatives of at least a dozen unions had participated in earlier exploratory talks encouraged by White House political operatives.

Even some of the six appeared more enthusiastic in their prepared statements than in answers to reporters' questions. Asked how he would rate President Carter's record on one of the administration's own internal report cards, the group's spokesman, William H. Wynn, said, "Fair."

Neither Wynn nor any of the others said what they would do if Kennedy got into the race, saying they accept Kennedy's statement that he is not a candidate. "We didn't come here to speculate about Sen. Kennedy," said Paul Hall,, co-founder of the group.

In addition to Wynn, who is president of the United Food and Commercial Workers, and Hall, president of the Seafares, the group included Sol Chaikin, president of the International Ladies Garment Workers; Murray Finely, president of the Amalgamated Clothing and Textile Workers; Glenn Watts, president of the Communications Workers, and Jack Otero, vice president of the Brotherhood of Railway and Airline Clerks. BRAC President Fred Kroll declined to participate.

Wynn's recently merged union, with 1.3 million members, is the largest AFL-CIO union. But bigger unions such as the United Auto Workers Teamsters and National Education Association are still on the sidelines. Two of the biggest blocs within organized labor, building traders and public employes, were not represented.

Some participants have reportedly reserved the right to reassess their positions if Kenndy jumps in, although Wynn said yesterday they will be "supporting President Carter every step of the way." Said Hall: "We don't fool around ... we play for keeps."

Some of the early supporters have strong reasons for supporting an incumbent. For instance, the Seafarers are heavily dependent on federal maritime policy, the two textile-apparel unions are indebted to the administration for recently negotiated import restructions, and the railway clerks union is lobbying intensively to prevent Amtark cutbacks. "Pragmatism plays a role in these things," said one labor source.

Nonetheless, this source and others say Carter will probably pick up widespread union support, if Kennedy does not run. Organized labor supported Carter in 1976 but became increasingly disenchanted, especially with his economic policies, prompting many union leaders to cast about for alternatives. The only alternative who has attracted them as Kennedy.

Hall said the pro-Carter effort is unique for organized labor this early in a campaign. "This president," he explained, "needs all the help he can (get)."

Speaking for the group, Wynn said Carter, "like Roosevelt, Truman, Kennedy and Johnson before him, has been a consistent, committed champion of working men and women," and has built a "solid record of achievement" while tackling difficult problems such as energy. He said Carter had supported labor issues like the minimum wage and said he would have rated Carter higher than "fair" if he had won congressional approval for the labor law revision bill last year. CAPTION: Picture, Carter at White House lunch yesterday; in foreground, Energy Secretary James Schlesinger., AP