The Great Peace March, the culmination of decades of transcontinental treks for every cause imaginable, limped bravely off today on the first leg of a 3,235-mile route littered with legal and financial obstacles.

Despite organizer David Mixner's announced intention to gather thousands of additional participants across the country and stage a triumphal finish in Washington on Nov. 15, marchers said they would be happy if the Great Peace March makes it out of California.

More than 1,300 marchers -- many of whom were westerners, people under 30, female or retirees -- headed out of a parking lot near the Memorial Coliseum shortly after noon today for a star-studded rally in front of City Hall, after which they planned to walk east to the campus of California State University, Los Angeles, for their first night on the road.

With actors Robert Blake, Ed Begley Jr., Marilu Henner and John Randolph in the lead, the marchers covered the first few miles singing, waving balloons and posters, pushing strollers and contemplating the difficulties of engaging the world in the struggle to destroy all nuclear weapons.

They largely ignored a few young counter-demonstrators from conservative and Christian groups chanting "defense is cheaper than war" and dropping small toys in their path to symbolize disguised landmines used by Soviet troops in Afghanistan.

Mixner, a veteran of presidential election campaigns, conceived of a cross-country march so large and well-equipped that it might bring a new urgency to efforts to abolish all nuclear weapons. Bleary from long days spent telephoning potential donors, Mixner hugged Blake and assured reporters that the internal fights and the shortages of funds, insurance and popular support would all pass.

Mixner's PRO-Peace (People Reaching Out for Peace) has spent $4 million on food and equipment and cannot afford at this time to support more marchers or buy the $5 million liability insurance demanded by state officials for use of highway routes.

California Highway Patrol Lt. John Kielbasa, leading the police escort up Figueroa Street, said local governments had waived insurance requirements for the first three days of the march. Alternate routes were being discussed for getting across huge, arid San Bernardino County without using the main highways.

But the marchers seemed impatient with talk of clout and insurance and permits and money.

Lynn Nadeau, 40, an instructor of English, said she decided to join the march when "I got to the last sentence of the first paragraph of the first article I ever saw about it." Her decision meant that Alexa Nadeau, 10 months old and teething, would be the youngest marcher; husband Pierre, a circus trampolinist, remained in San Francisco to earn the family living.

Clare Cattarin, 26, a registered nurse from Santa Cruz, Calif., who quit her hospital job to join the march, voiced few illusions. "It is just something I have to do," she said.

When the several dozen children on the march grow tired, plans call for driving them to a temporary day-care spot at that evening's campsite. Organizers had visualized a $20 million transportable city of 2,500 tents and 70 trailers with mobile kitchens, showers, laundries and clinics, moving 15 miles a day for 255 days. So far it is much smaller, but Mixner said he hopes for a full complement of 5,000 marchers (800 are on a waiting list) by the time they reach Denver.

When Mixner is reminded that a majority of voters in 1984 seemed to endorse the Reagan administration's approach to arms control -- balancing nuclear threats rather than destroying weapons -- he smiles. "The best thing about the American political process, the reason I love it so much, is how changeable it is," said Mixner, who played an important role in the 1968 campaign to dump President Lyndon B. Johnson and the 1984 presidential bid of Sen. Gary Hart (D-Colo.). "In 1964 people thought the conservative movement was dead," Mixner said. "Now we have the strongest conservative movement since the 1920s."