For most Americans, today's 101st annual observance of Labor Day marks a holiday from work, a chance for a backyard barbecue or a final summer beach trip, and a seasonal signal of the coming of the school year.

But for organized labor, today is not only Labor Day, but also Solidarity Day 3--the third year of a new four-year effort aimed at rebuilding labor's lost cohesiveness, showing that unions still have muscle, and flexing that muscle to topple the Reagan administration in 1984.

The AFL-CIO hopes to draw as many as 500,000 people today to 150 marches and rallies scattered throughout the 50 states. From New York to Chicago, and from the hamlet of Merrill, Wis. to the largely nonunion town of Charleston, S.C., the demonstrations will focus on opposition to Reagan's economic and domestic policies, and on demands for more jobs, job training, protection of key industries from foreign imports, "pay equity" for women whose work is believed undervalued, and other changes.

Solidarity Day 1, on Sept. 19, 1981, was the first major protest against the administration's domestic budget cuts and curtailment of social programs. A Solidarity march drew 250,000 labor and civil rights demonstrators to Washington, according to a crowd estimate by D.C. police. The AFL-CIO claimed 400,000 participants.

Inspired largely by anti-Reagan sentiment and partly by the stirrings of the Polish trade union Solidarity, the 1981 rally was labor's first mass effort at reactivating a labor-liberal-left coalition that has been in retreat in recent years. Organizers of last week's "Jobs, Peace, and Freedom" march honoring the late Martin Luther King Jr. have also said they hope their showing of 300,000 marchers will mark the rekindling of the same potentially powerful political coalition.

The Solidarity Day concept began largely because of growing antiadministration militancy among the rank-and-file, who feared for their jobs and opposed cuts in unemployment compensation, food stamps and other programs, union officials said.

The American Federation of Government Employees, for instance, had its first-ever "emergency political action conference" five months after Reagan's inauguration, and 400 local AFGE leaders recommended a national demonstration, according to Bernard Demczuk, a political organizer for the union, which, at 750,000 members, is the largest organized group of federal workers.

"That kind of anger about Reaganomics filtered up to the executive council of the AFL-CIO and they said, 'Let's do something,' " Demczuk said.

"The AFL-CIO had never done anything like this before," said Murray Seeger, the federation's information director. AFL-CIO President Lane W. Kirkland "had gotten tired of hearing Reagan say he had a mandate from the workers," Seeger said.

Kirkland held a series of regional conferences in 1981 to feel labor's pulse--a new idea that the federation now plans to continue annually--and came away with the belief that labor's ranks were sufficiently angered at Reagan to turn out in large numbers in Washington, Seeger said.

In contrast, today's Solidarity 3 activities are spread throughout the nation, partly because the AFL-CIO didn't want to attempt another Washington march just one week after labor had mustered an estimated 60,000 troops to Washington on Aug. 27 for the 20th anniversary civil rights march. The AFL-CIO has scheduled no activities here except the traditional Labor Day multidenominational morning mass at Sacred Heart Church in Northwest Washington.

Following that, a contingent of several thousand D.C.-area union members will attend an 11 a.m. march and 1 p.m. rally at Hopkins Plaza in Baltimore. In Virginia, there will be a march and rally in Covington, with a large contingent of paper workers from the Roanoke area.

"We intend to show we have a national presence with a demonstration in every state," Seeger said. "If you can get 5,000 or 10,000 people in Manchester, New Hampshire, that's as good as 100,000 in Washington."

"Some cities will be having their first labor demonstrations in 20 years," Seeger said. Kirkland and the AFL-CIO's only other elected official, secretary-treasurer Thomas Donahue, plan to hopscotch the nation separately today, appearing in New York and Chicago, and in less labor-oriented states such as Kansas, Arkansas, Texas and Nebraska.

Solidarity Day 4 is to be held on Election Day 1984, which may be the final test of how well the labor effort has worked.

In the 1984 elections, "labor by itself will not be able to defeat Ronald Reagan or turn Congress around," said Joslyn Williams, president of the Metropolitan Washington Council, AFL-CIO. "But in concert with other coalitions--like civil rights, feminists, liberal organizations--we will be able to turn the country around."

AFGE's Demczuk said he hopes the Solidarity Days will become an ongoing vehicle for renewing lost militancy. "It's very difficult to get back Labor Day as a day of very militant protest, when for 50 years it has been a day of rest or barbecuing," he said. "So we have to create a new day that is our own."

The AFL-CIO, however, has not decided whether Solidarity Day will become a permanent annual fixture for organized labor, Seeger said, "We are a little bit apprehensive about making it like Super Bowl 14 or Super Bowl 15. We haven't considered yet beyond 1984."