Washington — The Rev. Jesse L. Jackson stirs up crowds in every black community and church he visits these days. His grass-roots supporters chant ''run, Jesse, run'' as they urge him to go ahead in a bid for the Democratic nomination for the presidency.But the clear political fact is that a Jackson candidacy is not supported across the board by all blacks. As was shown at a recent meeting of the Congressional Black Caucus, there is an outspoken dissident group that doesn't want Jackson or any black to run for president ''at this time.''It includes:
* Black politicians. Many are already committed to candidates in the field. ''There is no monolithic unity among black politicians,'' says Rep. Ronald Dellums (D) of California, who seven years ago begged off when the National Black Political Party asked him to run as its independent presidential candidate. ''They have their own interests - some to local candidates and issues , some to a hoped-for winner. The bottom line is their own survival.''
* Civil rights leaders. Neither Benjamin L. Hooks of the NAACP (National Association for the Advancement of Colored People) nor John E. Jacob of the National Urban League endorses any black candidate running for president in 1984 . And the Black Leadership Roundtable, a volunteer group of heads of more than 125 national black organizations, met all day Sept. 24 without making a statement. The leaders are split.
* Black ''realists.'' They say now is not the time for a ''spoiler'' black candidate. They will not be quoted personally, but many say Jackson's running may spoil the chances of former Vice-President Walter F. Mondale to win the Democratic Party nomination. ''Go with the best possible candidate and most likely winner for us,'' they say.Though some civil rights and political leaders apparently do not favor a Jackson presidential campaign, they are not willing to speak out against such a run because of the current grass-roots support for the charismatic minister.Mayor Andrew Young of Atlanta may best express the attitude of the nonbackers. When asked if he has presidential ambitions of his own, he frankly says, ''I'm not interested.'' When asked about Jackson, he tempers his remarks:''I don't oppose the idea of a black candidate. But I don't like the idea of supporting a candidate just because he's black. This is counterproductive - doomed to defeat.''Jackson will ''make his own decision,'' Mr. Young says. ''He has popularized political issues, voter registration, and captured the public imagination. He articulates the interests of people - good strategy for 1983, but I'm not so sure about 1984.''Mrs. Coretta Scott King does not support the candidacy of Jesse Jackson. She has made no public comment, but apparently Jackson has read her message. During the 1983 march on Washington, she was the key person in the formation of the new Coalition of Conscience, replacing the old ''rainbow coalition'' of 1963. Jackson paid homage to the Coalition of Conscience in August, but now he speaks of a ''rainbow coalition'' in his presidential press conferences and speeches. Roy Innes, national president of CORE (Congress of Racial Equality), once a big name among civil rights organizations, remains silent on support for Jackson. It appears that Jackson may face the fate of former Rep. Shirley Chisholm of Brooklyn when she sought the Democratic Party nomination in 1972 - no support from the Congressional Black Caucus, limited backing by black politicians and the women's movement. She won only a scattering of delegates in the primaries. But Jackson has taken concrete steps to campaign. He has named Richard B. Hatcher, mayor of Gary, Ind., as chairman. Local political leaders are ready to set up campaign offices. Ministers have organized their congregations to provide manpower and fund-raising help at Jackson's call.And despite skepticism from some quarters, there is still plenty of support. M. Carl Holman, president of the National Urban Coalition, has endorsed a Jackson candidacy. So do such mayors as Mr. Hatcher and Johnny Ford of Tuskegee, Ala., president of the National Association of Black Mayors.Speaking of white support, Jackson says: ''We should not prejudice the case until we test it. Americans are willing to see people other than whites as leaders and role models. Look at what's happening now - a black astronaut in space, a black woman as Miss America. There is room for another historical breakthrough.''''I admire Jesse Jackson for even saying he may run,'' said one black cab driver. ''He can fight bigotry and hate. He'll open doors for us. He'll make paths for our young people.''