Thousands of supporters of the Equal Rights Amendment launched a major fundraising campaign yesterday with ERA walkathons here and in more than 50 other cities across the country in a final drive for the amendment, which must be ratified within the next 10 months, or die.

An estimated 2,250 to 2,500 participants in the walkathon here pledged $92,600 for themselves and others after trudging 10 miles around the Mall and Capitol. Organizers said the nationwide goal is $1 million to help bankroll the amendment lobbying effort.

With a June 30, 1982, deadline for ratification, the amendment -- which provides that "equality of rights under the law" must not be denied to anyone on account of sex -- needs to be approved by three more state legislatures to become part of the U.S./ Constitution. A constitutional amendment must be ratified by three-fourths, or 38, of the 50 states for adoption.

Yesterday, ERA leaders, wearing the green and white colors of the ERA movement, outlined a final strategy for winning ratification. They say it will entail about 1 million workers in a nationwide campaign to inform the public and influence key state legislatures about what the amendment means in terms of better job opportunities and government benefits for women.

"The more [women] realize this amendment means better wages, better Social Security benefits and better economic benefits in every way for women, the more they are for the Equal Rights Amendment," said Eleanor Smeal, director of the National Organization for Women.

Smeal listed economic issues that ERA supporters intend to make more widely known to the public in the next 10 months through rallies, marches, phone calls, direct mail campaigns and leafletting. Women, she said, earn 59 cents for every dollar a man earns, women get 55 percent less than men in Social Security benefits and a women with a college degree often earns less than a male high school dropout.

The final offensive will include reminding national leaders, including President Reagan, who opposes ERA, that the women's vote can be influential in future elections. Recent studies have shown that far fewer women than men voted for Reagan in 1980 and that their vote was tied specifically to his stand on ERA.

Molly Yard, a chief ERA strategist, said the women will also try to capitalize on recent surveys that have found more women than men are Democrats. "The Democrats would really stand to gain politically if they decided to lead the fight for ERA," she said.

Whether three additional states will approve the amendment is something not even Smeal is predicting at this point. The original deadline Congress set for ratification of the amendment was March 22, 1979, but then, after several states repeatedly rejected the amendment, Congress extended the deadline to June 1982.

Nonetheless, leaders of the women's movement say public support for ERA and the number of ERA workers has never been higher, and point to a recent Time Magazine poll that said 61 percent of the American public now supports ERA.

Smeal said ERA workers would work especially hard in the coming months to attract women on Social Security and college students to their cause.

Many of the people who participated in the walkathon yesterday will be recuited into "message brigades," networks of workers that the ERA leadership says it can depend on to participate in letter-writing campaigns to state legislators and door-to-door, direct mail and phone call campaigns to the public.

"We have to keep ERA in the national news . . . It has to be a campaign where a person cannot turn around without seeing some reminder of ERA," Yard said.

Smeal said ERA workers would concentrate their efforts in six states: Virginia, Illinois, Oklahoma, Missouri, North Carolina and Florida.

ERA "has a lot of strength" in most of those states, Smeal said. In Virginia, ERA supporters are hoping that the fall elections and the state's new redistricting plan will help their cause.

But feelings about the possibility of ERA's passage were mixed among the participants in yesterday's walkathon here.

"I'm very worried. We're running out of time," said Marjorie Zuckerman, a medical secretary from Rockville.

"I've spoken to a lot of women, teen-agers and working women -- even my own daughter -- who seem to have picked up on some of the more colorful stereotypes of what women's liberation is all about and missed the important points about ERA, that it will mean equal pay for equal work, the increased availability of day-care centers for working mothers," she said.

But Flo Van Orden of Salt Lake City, an excommunicated member of the Mormon Church, one of the biggest opponents of ERA, said she is "very hopeful . . . The people I know who support ERA are just ordinary housewives. I don't know any bra burners." Next to her, enthusiastic marchers chanted "Ratify ERA, Ronald Reagan go away," as they passed in front of the White House.

The walk began at Lafayette Square, moved east down Pennsylvania Avenue, around the Capitol, past the Supreme Court and Library of Congress, west on Independence Avenue, then around the Mall once before going to the Lincoln Memorial, and finally north on 17th Street to the Ellipse.

The walkathon attracted a crowd of mostly young, white women, some of whom wheeled their babies along in carriages.

Also participating in the walkathon was Esther Rolle, the star of the television series, "Good Times."

Commenting on the small number of black participants, Rolle said she believes many black women feel they "still have got a job to do" to achieve just racial equality.