At least 3,000 supporters of the Equal Rights Amendment rallied in Lafayette Park yesterday to launch their final push to win ratification for the amendment before the deadline for its passage expires next June 30.

The demonostration, one of about 180 scheduled to take place throughout the country yesterday in an effort to win grass roots support, was attended by such diverse groups as the Southern Baptists for ERA and Harvard Summer Interns as well as feminist actor Alan Alda, who buoyed the crowd's spirits with inspirational oneliners.

By the end of the three-hour rally, pro-ERA organizers had collected over $10,000 in donations from the crowd, which throughout the rally waved dozens of organizational banners sewn in the suffragist colors of gold, purple and white and filled the air with ERA chants.

"Cynics say the odds are against us; we know the odds are against us," said Eleanor Smeal, president of the National Organization for Women (NOW) at a pre-rally press conference. "But even if you said there's no chance at all there's reason to go forward . . . to show that this is a movement that will not be denied."

"You could win the battle for the Equal Rights Amendment and lose the battle for women's rights," she added.

Though the ERA has been ratified in 35 states, three more are needed before the bill can become part of the Constitution. In 1978, Congress voted to extend the deadline for ratification from March 22, 1979, to June 30, 1982, but no state has ratified the amendment since 1977.

Further clouding the chances for ERA's ratification have been the attempts by five state legislatures in the last six years to rescind earlier votes approving the amendment. In addition, legislators in two of those states have joined with those in a third to challenge in court whether Congress has the authority to grant an extension to all.

While NOW officials say they are confident that those attempts will fail, rally leaders nevertheless hammered repeatedly yesterday at the need for mammoth fund-raising and volunteer efforts in the months remaining before the new deadline runs out.

"If you care about yourselves, if you care about your life, if you care about democracy, don't leave here today without a job to do," said Alan Alda, who received several standing ovations. "Nobody can leave here today saying that my heart's in the right place. That's not going to be good enough anymore."

Smeal said that strategy for the ratification "Countdown" campaign will focus on state legislators in six of the 15 unratified states: Illinois, North Carolina, Oklahoma, Missouri, Florida, and Virginia. NOW officials say ratification in those states has been held up by small numbers of politicians. How successful those efforts will be, however, was the question of the day for ERA supporters and detractors alike.

"It's a dead issue," said Phyllis Schlafly, president of the nationwide Stop ERA organization, at a meeting with reporters before the rally yesterday morning. "I'd be happy to stop pushing the cadaver back in the coffin."

"I think they will continue to lose in the statehouses of this country because the American people do not want their scale of values, they do not want absolute equality between men and women," Schlafly aid.

ERA supporters said that the Reagan administration's opposition to ERA will generate more support for ratification in the coming years. "We started to notice a difference in response rate immediately after the election," Smeal told reporters. She said that new members have been joining NOW at the rate of 3,00 each week, twice as many as in previous years.