Ronald Reagan made the pilgrimage to a Teamsters union convention during his 1980 campaign for president, and in 1984 it was Vice President Bush's turn, as he journeyed to a Columbus, Ohio hotel to clasp hands with Teamsters President Jackie Presser and accept the union's endorsement.

"We couldn't be more pleased. We're very, very grateful, I'll tell you, and we will work, work hard to earn the confidence of your members," Bush told the cheering delegates of the International Brotherhood of Teamsters. "We're proud to be here."

Since then much has changed. Former Teamsters president Roy Lee Williams has testifed in dramatic detail about the links between the union and the Mafia. Presser has been exposed as a Federal Bureau of Investigation informant, and the government's decision to drop its criminal fraud investigation of Presser has been sharply criticized.

Now Republican strategists and potential 1988 presidential candidates may be forced to rethink the close relationship that has existed between the Republican Party and the Teamsters, according to labor and political analysts of both parties. But many Republicans are reluctant to discuss the matter publicly.

"It is a sensitive subject, and I have friends on all sides, and I would rather not discuss it, by kicking a group when they are down," said Lee Atwater, a top adviser to Bush who was deputy director of the Reagan-Bush campaign in 1984.

Said one GOP strategist: "Candidates will not be rushing out and seeking public endorsements from the Teamsters. But by the same token, in a national campaign they can deliver votes, so you have a paradoxical position of people wanting their votes, but not wanting their public support . . . because of the taint."

Ultimately, the crop of 1988 Republican candidates will help determine how valuable the relationship is. Marlin Fitzwater, Bush's press secretary, put it this way when asked whether the vice president's view of the Teamsters had changed since the last campaign:

"Our position is that the Teamsters union is made up of good, honest, hard-working people, and they have the right to choose their leaders, and we will deal with whoever those leaders are," Fitzwater said. "They are a large union and an important segment of society, politically and economically."

After Reagan's election, Presser was made a labor adviser and honored with a reception, a Reagan visit and dinner invitations to the White House.

As the 1984 campaign approached, White House counsel Fred Fielding advised the president's staff to keep Presser at "arm's length" because of the then-pending criminal investigation. Current and former administration officials say future contacts will be the subject of more heated debate in Republican circles.

The case for continuing the relationship comes from Edward J. Rollins Jr., the Reagan-Bush campaign director in 1984 and now a political consultant, who is negotiating to represent the Teamsters political action committee.

He said Presser was "a very good friend and will remain that" and noted that Presser had "put his money where his mouth was" by actively campaigning for the GOP and by influencing the Teamsters to support Reagan in 1980 and 1984.

Rollins estimated that the endorsement and political activity by the 1.9 million-member union were worth up to $6 million, but added that it had additional symbolic importance in demonstrating blue-collar support for Republicans. In contrast, the AFL-CIO's endorsement of Democratic presidential candidate Walter F. Mondale was estimated to be worth $20 million to $30 million in union mailings, advertising, telephone banks and manpower.

At 1984 Republican campaign stops in Ohio and New Jersey, Presser arranged for Teamsters truckers to line up in mile-long Reagan-Bush truck escorts, "and they had great shots for TV . . . you don't get any more blue-collar than America's truckers," said a Republican National Committee strategist who asked not to be identified.

Rollins dismissed allegations by Williams implicating Presser in illegal activities, saying "there have been a lot of allegations about Jackie in the past that have not been proven," and adding that he did not consider Williams to be a reliable source. "We have not reached the point of parting company [with Presser] and that is a judgment that any candidate will have to make in the future," Rollins said.

Teamster officials would not comment for this article. Several administration officials and former RNC officials discussed the Teamsters on the condition they not be identified.

"The record is perverse and unfortunate for everyone concerned," said a current ranking administration official who said there is "bad advice" given at the White House about maintaining ties with the union.

A White House official said that "you have to deal with [Presser]" on economic and political issues because of the size of the union, "but it is one thing to deal with him, and another to throw your arm around him and dance with them . . . It gets really bad when a candidate starts to be associated with a person who is not seen as a union leader, but begins to be seen as an unsavory character."

As a potential 1988 presidential candidate, "Bush would be foolish to abandon an organization of that size, with that political machinery," a former RNC official said. "It would be ridiculous. But to embrace the Teamsters right now would be pretty foolish too."

But he said that the same argument "could be applied to Mondale and the AFL-CIO. They get some bad publicity, but they can reach 3 million, 10 million people in a snap, and they have big bucks."

The Teamsters were expelled from the AFL-CIO in 1957, following allegations of corruption that surfaced at the Senate's McLellan Committee hearings. Those hearings resulted in the largest drop ever in public opinion about labor unions in the history of the Gallup Poll.

"The Teamster-Republican connection is a very perplexing association . . . that I find most peculiar," said Paul Jensen, Mondale's liaison with the AFL-CIO. In addition to financial benefits, he said, "I think they felt the symbolism was so important of having a union with them, that they were willing to stay with them, even with the liabilities."

Kenneth Paff, a spokesman for the Detroit-based Teamsters for a Democratic Union, which has long sought to oust Presser and Williams, said he believed that fresh revelations reinforce the impression that Presser is "widely discredited among the union hierarchy and now universally hated within the union."

Evidence of that, Paff said, is that Teamsters membership has verwhelmingly rejected two of the four nationwide contracts negotiated by Presser since he was named president in 1983, the first time members have ever rejected a nationwide contract in recent union history.

Labor Secretary William E. Brock was not available for comment. But a department official said that "when it first became known in 1982 that Presser was under investigation, people kept their distance. Brock treats Presser like any other union president, no closer, no further."