Washington — As the United States Senate prepared for the final vote, hundreds of supporters rallied outside, cheering for a constitutional amendment to permit vocal prayer in public schools. It was one more proof of the popular support for a practice overruled 22 years ago by the US Supreme Court.
But when all 100 senators had trailed in to vote, they soundly defeated the prayer proposal, giving only 56 of the 67 yeas required for amending the Constitution.
Both sides now agree that the amendment sank mostly because of its own weight. For two weeks the Senate had debated the emotionally charged proposal, which pollsters have said has the support of 80 percent of Americans. But from the start the supporters failed to describe exactly how the amendment would affect millions of schoolchildren, their teachers, and their schools.
''We didn't clearly spell out what this amendment meant,'' concedes Gary Jarmin, legislative director of the Christian Voice and a leading proponent of organized school prayer. ''We didn't seize the high ground in the debate.''
''It was confusion on the issue that helped us out,'' says one of the leading opponents, Kim Yelton, a lobbyist for Americans United for the Separation of Church and State.
School prayer forces in the Senate produced an array of possible amendments, including one to permit silent prayer, and then proposed amendments to those amendments. Even the Senate Judiciary Committee proved indecisive when it reported out two versions, giving its endorsement to neither.
Senate majority leader Howard H. Baker Jr. (R) of Tennessee, scrambling for a coalition to win the two-thirds vote needed, tried to forge together compromise language that would satisfy the waverers. But the language became unwieldy, and still there were doubts.
Questions arose about whether government officials would select prayers and whether students would be put under pressure to participate. At one point the Capitol was abuzz with talk of ''praying'' and ''no praying'' sections in the schools.
By the time the vote occurred Tuesday afternoon, the opponents, led on the Senate floor by Sen. Lowell P. Weicker Jr. (R) of Connecticut, were confident of victory. ''These were matters of deeply held convictions and belief,'' Senator Weicker told reporters after the vote.
He said that his side won because he was able to slow down the momentum of the prayer amendment drive. ''We needed to lay out our case,'' he said, citing his best argument as the First Amendment, the constitutional guarantee against entanglement of church and state.
Presidential persuasion failed to win enough senators for the prayer amendment, which has been a top priority of Mr. Reagan. Sen. Arlen Specter (R) of Pennsylvania, among those invited to the White House for a pep talk, emerged still opposed.
''I think the essential question turned on unanswered questions about who would write the prayer, what the prayers would say, and (whether) children of tender years could be subjected to prayers at variance'' with their religious faith, he said after the vote.
The question now is what the prayer supporters will do with their newly energized movement. Mr. Jarmin reports that his group will push for an ''equal access'' law,which he says would grant religious groups in schools the use of meeting rooms on the same basis as the glee club and other activity groups. Such a bill, which would require only a majority vote, would have an easier road through Congress.
Sen. Jesse Helms (R) of North Carolina, has served notice that ''we have just begun to fight,'' and said he will move to restrict federal court jurisdiction in school prayer cases. Past ''court stripping'' efforts have met entrenched opposition.
Both sides on the prayer issue foresee possible political aftershocks.
''I don't think you're going to let anybody who votes against prayer forget about it,'' Colonel Doner, an official for the Christian Voice, proclaimed to an applauding Capitol Hill rally.
Said Senator Specter, ''I think there is considerable risk of political fallout on this vote.'' However, he held that President Reagan's effort on school prayer had been ''sincere'' and declined to charge Reagan with using it as a political issue. But Weicker, asked if the White House had political aims in the prayer effort, responded, ''If the shoe fits, wear it.''
And Sen. James J. Exon (D) of Nebraska pleaded with President Reagan not to use the issue to blast opponents. ''I'm very much afraid that this matter will become a political football,'' said Senator Exon, who is up for reelection and who voted for the amendment.
However, a presidential candidate, Sen. Gary Hart (D) of Colorado, came off his campaign trail to cast a ''no'' vote on the prayer amendment and professed to be unafraid of political repercussions. ''In this case I have to vote by what I think is constitutional and right,'' he said, calling the prayer issue the ''politics of distraction to get people's minds off deficits and the arms race.''