Washington — ''The rainbow coalition is disproportionately black, and in places like New York City, Hispanic. Whites are not voting black in the primaries. And Jesse (Jackson) is running last in a three-man race,'' says Francesta Farmer, lecturer at the Institute of Politics of the John F. Kennedy School of Government at Harvard University and former director of the Congressional Black Caucus Foundation.
''Yet, I say, this (Jackson) campaign for president is a brilliant success,'' she quickly adds. The Rev. Jesse L. Jackson is ''leading black Americans into the promised land of real political power.''
''Whites may not cast their ballots for Jesse in the Democratic primaries,'' she says, ''but they will be tangentially influenced by the potency of the black vote, by the issues Jesse has raised.''
At the midpoint in the primary season, Mr. Jackson trails Walter F. Mondale and Colorado Sen. Gary Hart.
Still, Jackson is becoming a folk hero among black voters, but his major challenge remains: to broaden his appeal beyond blacks and Hispanics.
Since Jackson declared his candidacy last November, he has spoken of these basic goals:
* To convert a civil-rights grass-roots constituency into a potent black political power.
* To create a new political base, called the ''Rainbow Coalition,'' a combination of blacks with Hispanics, Asians, ethnic groups, peace advocates, and other disenchanted groups. This combination could become a power with either Republicans or Democrats.
* To present a unified front for black interests at the Democratic Party National Convention in July and the general election in November. This could expand Jackson's influence from that of a civil rights leader into that of a national spokesman for black people after the political season.
Jackson draws blacks to rallies and the polls wherever he campaigns, thus giving them political thrust. Some urban Hispanics have voted for him, but he is struggling to attract whites and others needed to make his rainbow coalition a reality. His clout at the July 16-20 convention probably depends on what he does in the remaining primaries.
Last week Jackson worked on his coalition - in Baltimore he stayed overnight with a white family, both parents unemployed, and in San Antonio he slept at the home of a Hispanic family in a public housing project.
Top officials in both cities - Mayor William Donald Schaefer and Rep. Parren J. Mitchell, Maryland's black congressman, in Baltimore, and Mayor Henry Cisneros, a Hispanic, in San Antonio - back Mr. Mondale.
Jackson captured the news media spotlight, both print and electronic, from Mondale in Baltimore. His approach - fiery speeches at rallies in and out of the city - proved more appealing than Mondale's endorsements from Mayor Schaefer and Representative Mitchell in a downtown ceremony.
''Our rainbow will come through,'' Jackson says, although he is disappointed in its slow takeoff.
At his national headquarters in Washington Jackson has added Donna Brazile to the staff as constituency coordinator. In her department overhead signs read ''Peace,'' ''Environment/Energy,'' ''women,'' ''Arab,'' ''Gay,'' ''Hispanic,'' and ''Jewish.''
Miss Brazile is the 23-year-old New Orleans native who packaged the multicultural, multiethnic, multiracial, and multi-interest support of the 1983 ''March on Washington'' last August.
''We feel good about our outreach,'' she says, ''but I'm hitting the road to meet people - college groups, ethnic groups, all voters. I expect to boost the rainbow with Northern liberals, Jews, Hispanics, everybody. I can't reach them sitting at a desk in Washington.''
Although whites are seated at several of the rainbow desks at national headquarters, most of the campaign office and traveling staffs are black. And it was the same at local headquarters in cities such as Philadelphia, Washington, Boston, Pittsburgh, and Baltimore.
Four whites are running in Baltimore as Jackson delegates to the Democratic convention, says Sandy Stewart, coordinator for Baltimore city and county. One, Howard Elsworth, spoke at a fund raiser in the black community.
At the primary campaign's midpoint, the black church is the backbone of the Jackson campaign. The Rev. Wendell Phillips, also a delegate to the house of the Maryland legislature, says, ''This is not just a political race; it's a crusade. I'm not a politician; I'm a preacher.'' He says 5 percent of the local white clergy are helping the Jackson campaign.
Off the record few supporters expect Jackson to win the Democratic nomination. Neither do they expect him to run for vice-president or run for president as an independent.
''Whites will not vote for Jackson in the primaries,'' Ms. Farmer says. ''He will influence the nation, however, at the Democratic convention, in the November election, and beyond that date.''
Jackson owes dues to few politicians, black or white - his ''partial endorsement list'' is less than two pages long. It includes only one big city mayor, Marion Barry of Washington.