From clerical workers in New York to furniture makers in Tennessee, from longshoremen in New Orleans to auto workers in Oklahoma, the nation's labor unions are playing a major role in organizing the 20th anniversary of the 1963 March on Washington that was a watershed in the civil rights movement.

On the grassroots level in more than 300 cities, local unions are distributing leaflets, chartering buses and peddling everything from cakes and cookies to fried fish and raffle tickets to build support for the Aug. 27 march.

On the national level, more than 30 major labor unions have endorsed and donated money to the march, two have given their Washington office space as march headquarters, and the AFL-CIO--which did not support the 1963 march--has strongly endorsed this one.

This prominent labor role is in marked contrast to 1963, when several major unions supported the march, but large segments of organized labor not only did not offer support, but in some ways opposed the goals of that year's march on Washington and resisted its aim of full integration of blacks into the American work force.

"Labor unions in 1963 were part of the overall pattern of racism in America," said Cleveland Robinson, secretary-treasurer of the New York-based District 65 of the United Auto Workers and one of the nation's highest ranking black labor officials.

"We have made a lot of progress since then," he added, "But we still have a long way to go."

Largely because of the gains of the civil rights movement that dramatically expanded black union membership, and due partly to the current high levels of unemployment, labor has moved squarely into the "new coalition of conscience" that 1983 march organizers have formed with religious, civil rights and peace groups, feminist and youth organizations and those representing the elderly, disabled and many other constituencies.

The national director of the 1963 march, the late A. Philip Randolph, who founded the Brotherhood of Sleeping Car Porters and the Negro American Labor Council, told the marchers then: "We are an advance guard of a massive moral revolution for jobs and freedom . . . and against poverty and unemployment."

But Randolph's vision, articulated at a time when blacks were growing more militant and the white-dominated labor movement appeared to blacks to be sluggish and cautious, clashed with the views of mainstream labor leaders such as the late AFL-CIO President George Meany.

The AFL-CIO and some of its more discriminatory unions were themselves becoming the targets of black protest.

Robinson of District 65, who served as administrative director of the 1963 march under Randolph and is now one of the national conveners of this year's event, recalled the fights against "whites only" unions in which the few blacks who broke the color barrier were relegated to the worst jobs.

"We were hitting hard at labor movement practices" in 1963, Robinson said.

"Now, the labor movement is way ahead of where it's been. Influential segments of labor are now well in step with the fulfillment of the dream of the late Dr. King Martin Luther King Jr ."

In 1963, the "jobs and freedom" dream of the march came at a time when the national unemployment rate was 5.5 percent, while black unemployment was close to 11 percent.

By contrast, the 1983 march--with the theme "We Still Have a Dream"--comes while national unemployment is roughly double that of 1963: almost 11 percent overall, roughly 20 percent among blacks, and far higher among black youth.

Much more than in 1963, labor is now experiencing the unrest of the jobless--black and white, blue-collar and white-collar, younger and older.

Their angers and anxieties have propelled unions into a more activist role, often in opposition to the Reagan administration, labor officials said.

"In 1963, we were talking about civil rights, poverty and unemployment. And now, that has really hit home for white workers" who face unemployment, said Minor Christian, president of the Washington-based Hotel and Restaurant Employees Union Local 25.

Christian, a member of the Coalition of Black Trade Unionists, said he found labor participation in the march "overwhelming, this time around" and attributed it partly to anger about President Reagan's policies and about the nation's slumping economy.

"You have unrest in the industrial states now . . . It hasn't hit as hard in D.C., but when you go to Chicago or Detroit, you really see it," he said. "The same concerns that were limited to blacks in 1963 have now caught up to white folks."

Twenty years ago, only a small group of unions with substantial black membership--notably the UAW, the American Federation of State, County and Municipal Employees (AFSCME) and the Service Employees International Union (SEIU)--endorsed and provided money for the march.

At the 1963 march, the late UAW president, Walter P. Reuther, delivered a stinging criticism of the AFL-CIO's refusal to join.

"The difference now is that we've seen a vast change of attitude about the effects of mass demonstrations," said Joslyn Williams, chairman of the Metropolitan Washington Council, AFL-CIO, whose 150 member unions represent 225,000 D.C.-area workers.

Since the civil rights and anti-Vietnam War movements showed the power of mass demonstrations, Williams said, "labor has forged a very, very strong alliance" with community groups in the belief that consolidated protest can effect change.

At the national march headquarters in the 16th Street NW offices of the National Education Association, Teresa Rankin, an AFL-CIO organizer assigned full-time to the march, coordinates the efforts of hundreds of local unions and dozens of internationals planning to participate.

"It's amazing how many unions are running 'local yokel' activities . . . using local union halls for meetings, and having local staff working" on the march, Rankin said. More important, she said, the AFL-CIO has thrown its full weight into encouraging support for the march.

March organizers, who peg the total cost of the march at about $500,000, estimate that unions, despite their own financial problems, will contribute more than one-third of that total, Rankin said, not including donations of labor time, and printing and distributing leaflets.

The AFL-CIO executive council endorsed the march last February "to advance and defend the great goals of the 1963 march in the pursuit of social justice."

The federation's president, Lane Kirkland, has followed that up with letters to unions urging their active participation--even though labor's own "Solidarity Day" activities are planned for Labor Day, Sept. 5, eight days after the march.

The logistical headquarters of the march, in the national office of the American Federation of Government Employees, coordinates everything from the effort to find housing for thousands of marchers, to the rental of hundreds of portable toilets and the assignment of several thousand marshals to greet the marchers at bus and train stations and to maintain order when more than 3,000 chartered buses arrive.

The D.C. government has assigned about 10 employes to the march, most of them working at the AFGE headquarters, where they direct the work of hundreds of volunteers who have offered to help distribute leaflets at Metrorail stops, act as marshals and perform other duties.

Mayor Marion Barry, who is expected to speak at the march, has assigned his labor liaison, Gwen Hemphill, to coordinate activities of city unions.

The Metropolitan Washington Council, AFL-CIO, has been distributing leaflets at some of the area's major work places for the past month to drum up support.

In addition to the leaflets, posters and banners, caravans of labor unions will be bringing to Washington a large number of "Resumes for Reagan."

This effort, in which thousands of unemployed people's resumes are to be delivered to the White House, grew out of a highly publicized incident earlier this year in which a jobless steelworker in Pittsburgh handed Reagan his resume, and the president found him a job.