HAZARD, KY. -- At Bailey's roadside restaurant here, Democrat Jesse L. Jackson was in search of "Super Tuesday" votes and -- right at the moment -- a piece of locally famous cornbread when a young mother thrust her pink-faced baby in his arms.

"Don't nobody dare tell him what this baby's named," squealed the nearby grandmother, who promptly blurted out, "her name is Reagan."

"Heal!" Jackson commanded, palm to baby's forehead in preacher style that drew whoops from the restaurant regulars in this eastern Kentucky hardscrabble hill country.

A campaign cliche for any other politician, Jackson's ease in an all-white, southern working-class crowd here neatly framed his central hope and hurdle: Will growing respect from whites turn into votes March 8 and allow him to break even further out of a racial box that was partially opened by impressive showings in largely white Minnesota, Iowa and New Hampshire?

In a five-day, 15-city, five-state southern tour this week, the South Carolina-born Jackson proclaimed himself a "son of the South who helped make the New South new." He hammered a populist message of putting people to work, stemming the flow of jobs to foreign countries and stopping the flow of drugs here.

In Hazard, a predominantly white crowd cheered when he offered his antidrug theme. Whites, sometimes only a handful, sometimes many more, cheered at nearly every stop. "You don't elect black or white. He's American. It's just that simple," said 18-year-old Robert Burton, a white business major at Hazard Community College. Burton will cast his first vote this year -- for Jackson, he said -- and was one of several hundred adults who cheered him at a campaign rally Thursday in the Hazard Memorial Gymnasium.

Many supporters are unemployed textile workers, farmers and union laborers who have become part of Jackson's coalition. Others are merely curious to see Jackson, and many say they do not know whom they will support.

Michael Mears, mayor of suburban Atlanta's Decatur and one of the few white politicians to endorse Jackson, said in Atlanta that Jackson's support is growing among blue-collar and middle-class white voters who spurned him four years ago.

"There was an image of Rev. Jackson as this flamboyant civil rights leader," said Mears. "It was difficult for him to get beyond that. But he has."

How far beyond is uncertain. After Jackson spoke to United Auto Workers leaders in Washington on Tuesday, Joe Mangone, director of the UAW's political arm, applauded Jackson's speech. However, he added, "They like Jackson's message. But they are also intelligent enough to know that for 1988 you can't elect a black president in America. Those are the facts."

Depending on news coverage -- "free media" -- for his low-budget campaign, Jackson's bottom line on Super Tuesday is elusive -- how many delegates can he expect from the rich lode of 1,307 at stake?

While some analysts say his strong base of black voters should help net him a minimum of 300 delegates, one Jackson strategist cautioned against projections. With four major Democrats dividing the votes, the complex congressional district method of awarding delegates, with its 15 percent threshold requirement, may be a major factor.

"The difference of a few hundred primary votes could mean a bunch of delegates for someone," said Steve Cobble, who is tracking delegate counts from Jackson's Austin headquarters for Super Tuesday. Just raising his vote a few percentage points among whites could have dramatic effects, said Cobble.

Staff aides pointed to expected strong showings in the deep South -- Georgia, Alabama, Mississippi and Louisiana. Jackson is second in the polls in vote-rich Texas. In the closing days to Super Tuesday, Cobble said Jackson will sweep again across the South and campaign "a little bit in the border states."

As he campaigned across the region this week, Jackson drew praise from blacks and whites who applauded his issue-laden message as well as his refusal to join the bickering among the other Democratic candidates.

Jackson concedes his approach has meant less free media coverage for a campaign that cannot afford costly but often crucial television ads. He blames the media for "concentrating on the trivial. In time, the more honorable my approach is, the less chance of the media blowing it out of the water."

In an interview, Jackson said he has broadened his message to appeal to a middle class that feels more economically threatened than it did four years ago. "This is not just the poor suffering -- the so-called underclass. As your constituency grows, it does obligate the message to be more inclusive."

He said he is appealing to the pride of southerners while trying to point to the poverty and problems that lie behind it.

In Eastern Kentucky, where local residents said he was the first Democratic presidential candidate to visit since Sen. Robert F. Kennedy before his 1968 campaign, Jackson said, a "false face of poverty exists . . . not just black . . . . {It's} white, female, young and former industrial workers. That is the truest face of poverty."

As a Jackson motorcade rolled into the Kentucky mountains to view the effects of strip mining, Jackson pointed to ramshackle homes squatting on the hillsides. He said it reminded him of the "hills of South Africa" and said the powerful coal interests were little better here than in that country.

In Ashville, N.C., white Republican Mayor Louis Bissette went beyond routine courtesy remarks in welcoming Jackson to an audience of several hundred, saying, "Rev. Jackson has earned my respect over the years and I think the respect of all Americans, black and white."

But Jackson privately chafes at the refusal of some big-name Democats in the South to back his candidacy, such as Sen. Terry Sanford (D-N.C.), for whom he worked when he was fresh out of college. Black votes helped elect Sanford, Jackson noted. But he declines public criticism. "{I} certainly don't overreact to it and give them another reason not to support you," Jackson said.