Charleston, S.C. — It's his fourth city of the long campaign day, but Jesse Jackson sprints up to the platform of Emanuel African Methodist Episcopal Church here, flashing victory signs and a glowing smile.
''Jesse, Jesse, Jesse,'' the crowd chants. The Democratic presidential candidate strikes instant rapport with the audience in his home state of South Carolina.
The poor ''clean other people's houses and cannot clean their own,'' says the Baptist minister. His listeners respond ''Yes.''
''They raise other people's children . . . ,'' he continues.
''. . . and cannot raise their own,'' he says, as the congregation cheers.
Those cheers have translated into some of the most enthusiastic black participation in elections ever. In South Carolina Democratic caucuses last weekend, black support gave him more votes than any other candidate, 25 percent of the vote, based on 80 percent of the returns.
''Our campaign has registered more new voters than anybody,'' says Mr. Jackson after his speech.
But as he takes his revivalist crusade through the South, the question remaining is what will happen to these newly mobilized voters when Jackson's ''Rainbow Express'' reaches the end of the road and another candidate is nominated.
The question is even more pressing when Democrats discuss the possibility of Gary Hart as the party's choice. So far his black support has been negligible.
''You can do without Gary Hart,'' Jackson tells the Charleston crowd. ''You don't even know him.'' The audience cheers in agreement.
Because blacks vote overwhelmingly Democratic, a big turnout is key to a victory for the party in the South. In 1980, voter participation dipped to a new low, and many blacks sat out the election.
''We know how badly low turnout hurt us,'' says Georgia state Sen. Julian Bond, a Democrat and longtime civil rights leader. ''Every southern state Jimmy Carter lost he could have won. Registered black voters could have made the difference.
''I think it will depend on Reverend Jackson and what he does,'' says Senator Bond, who traveled to South Carolina to campaign for Walter F. Mondale. ''If Jackson goes out and says, 'Come on. The elections are still going on,' then they'll come out in large numbers.''
Other blacks are less optimistic. ''I'm worried about the consequences of his (eventual) dropout - the letdown in the black community,'' says Isaiah Bennett, a Charleston labor union leader.
However, there are signs that even before Jackson began his campaign, blacks were registering to vote in growing numbers. The Voter Education Project, a private, nonpartisan group based in Atlanta, reports registering 329,000 blacks in the South during 1983. That is nearly twice as many as in the previous year.
Black registration ''was on the upswing,'' says project director Geraldine Thompson, but she adds that Jackson has helped. ''As a result of the enthusiasm that he has created, a lot has happened.''
Jackson's candidacy has attracted many blacks who have ignored politics in the past. ''I notice a definite interest,'' says Steven Derricotte, of fellow students at Trident Technical College in Charleston. ''Now they feel like they've got some personal interest.''
''Historically, getting on with some white who's become president hasn't helped us significantly,'' asserts his father, Marshall Derricotte. ''Jesse's got a brand new game. He's going in with delegates (to the national Democratic convention). He can speak as a broker.''
But will such Jackson support yield a big black vote for another Democrat next November? ''It depends on how damaging the Democratic convention is going to be,'' says Robert Ford, a black City Council member in Charleston and longtime Jackson associate. 'If they adapt in the platform things (Jackson) he wants, then he's going to go around the country'' supporting the nominee.
Jackson himself is giving only broad hints about what he wants from the party. In Charleston he said that ''the people that we are arousing are now in search of a candidate'' committed to issues such as social justice. He added that both Mr. Mondale and Senator Hart have a commitment ''at some level.
''I shall keep their feet to the burner,'' Jackson told reporters. ''I'll be fighting to the end.'' But if the end brings a Hart nominee, Jackson will have a lot of bridges to build to blacks in states such as South Carolina.
Among blacks here, a typical comment on the Colorado senator came from school teacher Thelma Williams. ''Really, who is he? He's been a senator. I've never heard of him (before his primary victories).''
The elder Mr. Derricotte, wearing his Jackson button on his lapel, put on a Mondale button as well. The former vice-president's button was lower, indicating second choice, he explains.
At the Bond rally for Mondale, which drew only 50 persons, several blacks said they support Mondale because of his ties to the late vice-president Hubert H. Humphrey. Hart has no such tie.
''If Hart is the nominee, I don't know what's going to happen,'' says City Councilman Ford. ''The blacks will vote for Hart, but what kind of turnout?
''The only black support Hart will get is traditional Democrats who've been voting Democrat all their lives.''
Disputing that view is Charleston Mayor Joseph Riley Jr., a Hart backer who has strong support in the city's black community. If Hart is nominated, blacks will vote heavily ''because it's going to be against Reagan,'' he says, adding of Hart that ''on the issues, he's been where they would want him to be.
''Often people who have been on the outs are more apt to get excited about someone who represents change.''