The first name of the president of the Service Employees International Union was published incorrectly Sunday. He is John Sweeney.

This week's meeting of the AFL-CIO executive council has made it virtually certain that organized labor will endorse a candidate for the Democratic presidential nomination before the end of this year. Unless he stumbles badly, that candidate will be Walter F. Mondale.

His only current threat, Sen. Alan Cranston (Calif.), slowed the rush to Mondale by dramatically asking the union leaders to tell him to his face if they were going to deny him, a longtime ally, a chance to overtake the front-runner. But that was a tactical victory that may not do more than defer the date on which Mondale gets a push from labor strong enough to power him through next winter's primaries.

The closed-door confrontation here with Cranston, which left tough union presidents impressed and shaken, was but the first of many obstacles past which federation president Lane Kirkland must maneuver his sometimes quarrelsome barons to achieve his dream of throwing the 14-million member labor movement and its nationwide political apparatus behind one candidate.

Reflecting the widespread concern that the pressures of presidential politics may aggravate ever-present interunion and intraunion rivalries, Robert Georgine, head of the building and constructions trade department, said, "I'm just hoping these two years go by without too much damage. What we're doing is new, different and experimental, and any time you do something for the first time, there are risks."

Despite such fears, Georgine and virtually every other labor chieftain agreed this week to move ahead on the Kirkland timetable that sets the endorsement decision for a December meeting of the general board. There was even some willingness to consider advancing the decision date to the October convention, an option still open to Kirkland.

Theoretically, the AFL-CIO still could back off if a serious internal split is threatened, but that escape clause is becoming less and less attractive. "We'll never know who we are or what we are until we try it," Machinists Union President William W. Winpisinger said. "Either we succeed, or we find out the shocking truth that we stink."

The presidents of the mass membership unions whose weighted votes will decide the endorsement were almost unanimous in saying this week that if the decision were made today, Mondale easily would win the required two-thirds majority.

His support stretches from such liberal bastions as the Machinists and United Auto Workers to the more conservative building trades and maritime unions, who still play footsie with the Reagan administration. It reaches from high-tech communications workers to growing ranks of service and public employes.

It is solidified by 15 years of partnerships, back to the Hubert H. Humphrey campaign of 1968 when labor made its last big plunge in presidential politics.

The only challenger who can begin to match Mondale's labor credentials is Cranston, the barefoot jogger who covered this gathering like sand covers the beach. But he is far back in national polls.

The only challenger close to Mondale in the polls, Sen. John Glenn (Ohio), chose virtually to ignore this meeting.

He seemed as remote from the hearts of union leaders as the quartet of dark horses--Sens. Gary Hart (Colo.), Ernest F. Hollings (S.C.), Dale Bumpers (Ark.) and former Florida governor Reubin Askew--who have records flawed by labor's standards.

Cranston made it as tough as possible for this crowd to forget what he has done for them as assistant Democratic leader of the Senate. Courting the unionists from beach to barroom to council chambers, he played hardball in his formal pitch for a fair chance to show what he can do to close the gap on Mondale.

"You owe me that," he told them in an eyeball confrontation that left many of the toughest union bargainers impressed. Cranston risked ridicule by courting the unionists all week. "When you needed your laundry done, Cranston was there," said Phil Sparks of the American Federation of State, County and Municipal Employes (AFSCME).

"When you needed a towel at poolside, he was there to hand you one."

But there was no kidding Tuesday morning when he faced the executive council, cited his 94 percent rating over the last 14 years on issues important to labor, his leadership on labor law reform and other issues and said that "if your endorsement is locked up for Mondale, as some people seem to think, I'm entitled to hear it straight from you."

It was Kirkland and Co. who blinked at the challenge, assuring the Californian that "you are not wasting your time." As evidence of good faith, at least five unions agreed to put the legal maximum of $5,000 apiece into Cranston's campaign kitty to help him contest Mondale's lead.

The result was a Cranston tactical victory: a decision Friday that no international union will make any endorsement at least until August. This blunted Mondale's plans to set a bandwagon rolling by collecting support of the million-member AFSCME in May and other unions soon thereafter.

But even such an ardent Cranston fan as Winpisinger concedes that unless Mondale stumbles badly in the next few months, the endorsement is almost certainly his. Meantime, he said, the pressure from a liberal such as Cranston "will help keep Mondale honest."

In 1980, Winpisinger was a key figure in labor's civil war, backing Sen. Edward M. Kennedy (D-Mass.) while most of the unions stayed with President Carter and a few went for California Gov. Edmund G. (Jerry) Brown Jr. Labor similarly was split in the 1972 and 1976 nomination battles, leading to what Winpisinger called "a lesser of two evils syndrome," in which the federation officially was neutral in the 1972 McGovern-Nixon battle and less than enthusiastic about its endorsement of Carter in his races with presidents Ford and Reagan.

Because most of the veteran union presidents agree with the service employes' William Sweeney that "if this endorsement is achieved, it will be the strongest labor endorsement ever made," many have obtained their governing boards' agreement to support the AFL-CIO choice in the primaries, whoever it is.

But for the labor federation, an agglomeration of disparate interests accustomed to going off in all directions politically, this new effort at discipline is causing severe strains.

In 1968, the last time big labor got into the pre-convention Democratic infighting with both feet, AFL-CIO President George Meany simply announced that he was backing Humphrey over Robert F. Kennedy and Eugene J. McCarthy for the nomination.

Now, the far less autocratic Kirkland is trying to guide his often fractious colleagues toward a freely expressed "consensus," while trying to keep them from making their deals independently. It is not easy.

While blocking AFSCME President Gerald W. McEntee's plan for a May endorsement of Mondale, Kirkland agreed Friday to allow individual unions the "maximum degree of flexibility" on grass-roots political activity in the 10 months before the AFL-CIO endorsement. Already, local unions and their activists are choosing up sides and pitching in for their candidates in such early caucus and primary states as Iowa, New Hampshire and Massachusetts.

The "flexibility" doctrine may extend even to individual unionists running for delegates on slates pledged to candidates other than the AFL-CIO endorsee. McEntee, for example, said AFSCME members in Florida have told him "they have to be on the Askew slate to get elected as delegates."

Noting that similar demands can be expected from other states with strong favorite-son candidates, the communications workers' Glenn Watts said, "Hell, some people would pledge to the devil to get to be delegates."

The inclination of most union presidents is to bow to such demands, rather than risk a disciplinary effort that could cause them political problems within their unions. The rationalization offered by many is that union delegates are union delegates, even if they come under the banners of different candidates.

That means, as a practical matter, that even if the endorsement comes through in December, there will be cases in which members will be fighting each other in the primaries.

But the rules adopted Friday forbid any state labor federation from making an endorsement. They put the machinery of the AFL-CIO on hold until the time when all the political clout of its Committee on Political Education (COPE) will be thrown behind the endorsed candidate. Mondale, Hart and Askew have rejected cash contributions from any such political action committee, a public relations gesture that offended some members of the executive council.

But COPE's power comes from the manpower it can generate and access to dues funds for communicating with union families and turning them out to vote.

That is why the endorsement can be such a boon to Mondale amd why he had former secretary of labor Ray Marshall and two Marshall aides lobbying for him here. In many cases, they found themselves preaching to the choir.

"There's broad support for Mondale," said William Wynn, president of the 1.2-million member United Food and Commercial Workers, which backed Carter last time. "He has an excellent record."

The United Auto Workers' Douglas Fraser, a Kennedy backer last time, said his "Ohio guys lean to Glenn, and the Californians are very close to Cranston, but overall, it's Mondale. Our Iowa people are very much that way."

The communications workers' Watts, with 585,000 votes, said, "If we took a poll right now, Mondale would be right up in front. He'd beat Glenn in Ohio, and he'd beat Cranston in California at this point. He's our very good friend."

In almost identical terms, Georgine, the head of the building trades department that includes almost one-third of the total membership, said, "I have worked with Fritz Mondale for many, many years. He is a close friend, and I have a great deal of personal respect and admiration for him."

There is concern here, as elsewhere, about Mondale's ability to excite voters. "There's no enthusiasm for Mondale," complained the American Federation of Teachers' Albert Shanker, who also criticized Mondale's support of affirmative action hiring programs.

Shanker, a Kennedy man last time, is also troubled by Mondale's close relationship with the rival National Education Association, which is outside the AFL-CIO and plans its own endorsement, presumably of Mondale, in October.

Winpisinger remarked that "front-runners have a nasty way of self-destructing, and Mondale is certainly not without baggage." He also said Mondale has "demonstrated a tendency to swerve right."

Notwithstanding all of that, he said the former vice president had topped a poll taken by Winpisinger of 150 machinist political organizers early this month while Cranston had "insignificant support."

Given the force of the pro-Mondale tide since Kennedy pulled out of the race, Cranston did well here just to keep things frozen. In contrast to Cranston's full-court press, Glenn left advocacy of his cause almost entirely to communications workers vice president Marty Hughes, a friend from Cleveland.

Howard D. Samuel, head of the AFL-CIO's industrial union department, said, "Some of our union leaders are afraid that Glenn will be more electable than Mondale. He's got what Mondale hasn't got, that hero status."

But most comments were in the vein of the service employes' Sweeney, who said, "John Glenn has not related so far to the issues our people care about. He's stayed with the non-controversial issues and tried to make as broad an appeal as possible."

Robert J. Keefe, a veteran labor-Democratic operative advising Glenn part-time, did not bother to come here for his client. In a telephone interview he said:

"Glenn suffers from the fact he has not been around these guys for 15 or 20 years like some of the others. The labor guys don't feel like they know him . . . . He's got to start getting them into his office for long lunches, a few at a time. He's got to do that right away."