Will Jesse Jackson run?

Jesse Jackson. It's a name that could go down in the history books when they write about the 1984 presidential election. Within the next few days, Mr. Jackson - a controversial and eloquent civil rights leader - is expected to decide whether to enter the Democratic race. If the answer is ''yes,'' it could send shock waves through several campaigns, especially that of Walter Mondale.

Huddled with aides this week in a Washington hotel room, Jackson was taking one last look at the things he needs to make a race. He calls them the three M's - money, machinery, and masses.

Jackson wants at least $3 million in contributions, a top-flight campaign team, and enough indications of popular support to ensure that his race will be more than symbolic.

If the pieces come together, experts here say it will bring about several things:

A setback for Walter Mondale. In the South, and in several major industrial states, Mr. Mondale is relying on overwhelming black support to gain the nomination.

His strategy in the South, where he faces a stiff challenge in the early primries from John Glenn and Reubin Askew, could be upset. A recent ABC News poll shows that with Jackson in the race, Mondale draws only 37 percent of the black vote.

A split in the black community. Jackson has enthusiastic support among many blacks.

But the black leadership is generally cool toward him. They see him as too ambitious, too self-centered, a loner. They also worry that if Mondale is elected without solid black support, he will feel that he owes blacks nothing.

A boost for other Democrats, especially John Glenn. By splitting Mondale's vote, a Jackson candidacy could help Glenn or another Democrat edge past Mondale in the early primaries. Jackson is aware of this, but considers Glenn just as acceptable to blacks as Mondale.

How much appeal does Jackson have?

Pollsters have been probing that question as Jackson stumped the country in search of support.

There is little doubt that if Jackson announces, he would immediately move up to third or fourth in the polls - ahead of such longtime candidates as Alan Cranston, Reubin Askew, Gary Hart, and Ernest Hollings.

Two recent surveys by The Garth Analysis, a New York political research outfit, found Jackson drawing from 7 to 10 percent of all Democratic voters. Most of that strength is in the black community.

Jackson aide Frank Watkins says the campaign, to reach its full potential, would attempt to draw together a ''rainbow coalition of the rejected.'' In this group, Jackson includes in addition to blacks, American Indians, Hispanics, peace activists, Pacific Americans, and others who feel left out of the American mainstream.

Jackson's campaign would be precedent-setting for black Americans. Yet many leading black Americans are urging him not to do it. They concede that they would like to see the big crowds, the press coverage, the black face on TV. But in the long run, as one veteran civil rights leader told the Monitor, ''we recognize that Jackson will not be the Democratic nominee.''

Another well-known black leader, who asked that he not be named, says:

''We want to be part of the real show, and not a sideshow. Most blacks really prefer to support a major candidate, one who has a chance of going all the way to the White House.''

Officials of the National Association for the Advancement of Colored People feel so strongly that Jackson should stay out of the race that the board of directors passed a resolution urging that all blacks avoid any action, ''however symbolically attractive,'' which might ''dilute'' the black vote.

The reasons go deeper than that, however. Jackson isn't very popular with many leading blacks who have worked closely with him. Jackson, a protege of civil rights champion Martin Luther King Jr., even managed to upset Dr. King at times, according to those who knew both men.

None of this seems to have dampened man-in-the-street enthusiasm for Jackson. He repeatedly has won polls among blacks as the ''most admired,'' ''most effective,'' ''most popular.''

Jackson hopes to turn that popularity into a drive that will excite blacks and other minorities in record numbers. His goal goes beyond his own campaign, he says.

He predicts that his effort could result in registering 3 million more black voters - a 25 percent increase over present levels.

Further, with Jackson in the race, all candidates, Democrat and Republican, will be forced to the left, forced to deal with the issues of race and discrimination. Thus, no matter who is elected, blacks will be better off after 1984, he argues.

All those newly voting blacks, he says, would also boost the number of elected black officials - and it's the sheriffs, the school board members, the city councillors who can really turn things around for minorities in America.

Jackson has shown that he knows how to turn things around in his own life.

Born in poverty in Greenville, N.C., Jackson had a difficult early life. Taunted by other children because his mother and father were unwed, Jackson made up his mind early that he would prove himself.

A three-letter athlete in high school, Jackson was offered a contract with the baseball New York Giants.

But he turned it down to go to college. He graduated with a sociology degree from the Agricultural and Technical College of Greensboro, N.C., and then went on to become an ordained Baptist minister before going to work for Dr. King.