C.O. Smith was incorrectly identified yesterday as Georgia Democratic chairman. He is chairman of the Mondale-Ferraro campaign in Georgia.

In July, Jesse L. Jackson promised a "signal" to his followers to lead them through the presidential election.

Jackson's signal to his Rainbow Coalition is: Register and vote.

Speaking to overflow audiences, he adds that there is more at stake than the White House.

Even if they are not excited by Democratic nominee Walter F. Mondale, they should vote for him, Jackson is saying, because Nov. 6 is "your shopping day for four years of political leadership."

The thrust of his speech is not an endorsement of Mondale but attacks, funny and sad, on President Reagan as stuttering and choking on the "sleaze rising" around the administration and as taking away scholarships and school lunch programs even as he tells schools, "Let us pray."

Jackson has begun to broadcast that lukewarm signal for Mondale in an energetic campaign schedule that took him to four states in three days last week for more than a dozen rallies. He is revving support among the black and young white voters Mondale needs to win on about $200,000 supplied by the Democratic National Committee for a month of campaigning. Jackson is also getting money from state Democratic parties and the Mondale-Ferraro campaign.

His relations with the Mondale campaign have been chilly to cordial, according to both sides, since Mondale ignored most of Jackson's demands for pledges on a jobs program and increased black participation in the campaign. Nonetheless, Jackson is being a good soldier for the party while keeping himself in the national political picture.

"TV only focuses on two heads, Reagan and Mondale, and makes it into a personality contest . . . ," Jackson tells crowds as large and feverish as he saw during his bid for the Democratic nomination. "If they were advertising food, it would make you think there were only cabbages for sale. If you didn't like cabbage, you wouldn't go to the store.

"But there are thousands of reasons to vote and no reason not to vote," he adds. "There is also meat, sugar, macaroni, vegetables and drink in the store . . . . We're not only voting for the White House, but the state house, the House of Representatives and the governor's house."

Jackson's message is coming through loud and clear in the South where state Democratic officials speak reverently of Jackson's power over black voters and of his ability to draw huge crowds. Jackson continues to bring in larger audiences than Mondale in most southern states and big cities across the nation, according to party officials.

Particularly in the South, Democratic officials, with a history of taking black voters for granted and not supporting black candidates, are busily courting Jackson as the key to ensuring that blacks will turn out for Mondale and abort independent black candidacies for state, county and local offices that could slice away the Democratic margin of victory over Republicans.

Southern party leaders also report that attempts to organize for Mondale in the black community this fall ran into the response: "We're waiting for Jesse's signal."

"They southern Mondale officials found out they have to negotiate through the Rainbow Coalition when they tried to go it on their own," Jackson said.

"It's been tough getting together here with the Mondale campaign," said Georgia state Rep. Tyrone Brooks (D), who headed Jackson's primary campaign in the state. "We fought them tooth and nail. Right now it's like your mother told you to go over to your cousin's house and you don't like him but you've got to be nice. They need us. We need power in the party . . . . "

Forgotten for the moment are differences between Jackson and southern Democratic officials about his angry fight with the party to end runoff primaries that he claims discriminate against black and female candidates. Forgotten is talk of a white backlash against Jackson in the South.

"Nearly a quarter of the people here today registered to vote," said C.O. Smith, chairman of the Georgia Democratic Party, after listening to Jackson speak at Morris Brown College in Atlanta. "We cannot carry Georgia without a strong turnout from blacks. That means we want Jesse Jackson coming in here whenever we can get him . . . . He's on the news; he's stirring up young people black and white for Mondale.

"The people who feel that they don't like Jesse," added Smith, "we couldn't change them anyway. They are a minimal factor. We want to get our people excited. With Jesse coming in today our office was inundated with calls."

In Little Rock, the day after his 43rd birthday, Jackson was presented with 43 cakes and a boisterous version of "Happy Birthday" sung by about 2,500 people.

At Emory University in Atlanta, a mostly white audience was on its feet for Jackson. Over a hundred of them walked down packed aisles to register to vote against Reagan.

"Nobody, nobody gets the response in this state that Jesse Jackson gets," said Arkansas Gov. Bill Clinton (D). "That goes for white and black . . . . The last time he came through here registration shot up; it took two weeks to calm things down."

Jackson, meanwhile, maintains loose ties to the Mondale campaign. He regularly calls Mondale campaign manager Robert G. Beckel and occasionally Mondale. But he has made only two appearances with Mondale: at a gathering sponsored by the Congressional Black Caucus and at a get-together in Lovejoy, Ga., attended by major southern Democrats.

The Mondale campaign's discomfort with Jackson was revealed in preparations for the first presidential debate. Jackson had proposed that he join Mondale in Louisville, along with other Democratic officials, to attend a labor rally for the Democratic candidate. The Mondale campaign, according to sources, turned down the idea.

However, when word spread of a black minister's plan to endorse Reagan in Louisville -- with the national media in attendance -- the Mondale campaign asked Jackson to come to Louisville to appear on network television news shows after the debate.

But two days before the debate there was concern that Jackson's presence might highlight Mondale's shortcomings as a debater. Jackson did not go to Louisville.

Tension between Jackson and Mondale peaked after the Democratic National Convention in July. Jackson had delivered the conciliatory speech Mondale had sought for the convention instead of railing against the party for not giving him delegates equal to his share of the popular vote.

Jackson then asked for commitments from Mondale to black Americans on job programs as well as on appointing blacks to key positions in his campaign. Mondale turned down the requests.

"I try to keep politics in my head and not let it get to my heart," Jackson said about Mondale's response. "The people saw the convention; they can judge. I can't talk now. I'll have more to say after Nov. 6."

Meanwhile, the Rainbow Coalition is acting as if Jackson may run in 1988. Jackson's response is that it's "too early to decide." But he boasts that his followers have remained loyal and that state Democratic Party chairmen, particularly in the South, deal with the Rainbow Coalition as a "power" group that is able to deliver its rank and file.

"The question is whether they [white Democrats] can deliver for us," Jackson said.