New York — The United States will have a black president ''probably within my lifetime, '' says John E. Jacob, president of the National Urban League. And, he says, the candidate who has initiated the momentum for sending a black to the White House is the Rev. Jesse L. Jackson, who looks to a patchwork ''rainbow coalition'' of racial, ethnic, and single-cause minorities for votes.
But Mr. Jacob warns that the Jackson campaign is ''hardly enough'' to make a dent on social ills that create a widening income gap between blacks and whites. He cautions:
''The projection of a black president at some time in the hazy future is not enough to offset the many ills and problems blacks face today: poverty, inferior education, political frailty, and unenforced civil rights.''
Jacob pauses, then reflects on ''another America,'' one not included in President Reagan's ''rosy'' State of the Union address in January. He has harsh words for the President.
''Reagan heads both Americas, but addresses only part of his responsibilites to the second America. I see black people as hurting very badly.''
Jacob steps to his desk, and picks up a copy of ''The State of Black America 1984,'' a 186-page National Urban League report published Jan. 19.
This study, a review published annually by the league, spotlights six key concerns of blacks: an economic recovery that does not include blacks; a high-technology industry that provides few jobs; households headed by single black women who are trapped in poverty; the black vote - a ''sleeping giant''; poor-quality urban education; and lax enforcement of civil rights.
Thumbing through the pages, Jacob mumbles, ''We can't brag about a reviving America that neglects the needs of 12 percent of its people! This book is hardly the story I like to tell during Black History Month.'' February is Black History Month, as observed by the national Association for the Study and Life of Afro-American History.
Six months ago Jacob did not believe that Jackson or any black could be more than a ''curiosity factor'' as a presidential hopeful. He openly expressed his doubts at the National Urban League Convention last August, and repeated his views in his weekly column, ''To Be Equal,'' appearing in black newspapers throughout the nation in January.
Now that Jackson has plunged into the race for Democratic Party nomination (a Chicago Sun-Times poll published Wednesday shows Jackson tied for second place with John Glenn among Democrats planning to vote in the March 20 Illinois primary), Jacob has altered his outlook.
''Jesse moves America ahead many years in preparation for a black president, '' Jacob intones softly, as he relaxes in his office on Manhattan's East Side. He does not endorse the Jackson candidacy, however. And the National Urban League does not officially endorse candidates.
''I'm not saying there will be a black president in 1984 or 1988. I say it will come a lot sooner than anyone anticipated a year ago - probably within my lifetime.''
Jacob points to the ''top stories'' of 1983, as noted by some of the nation's black media, including Ebony and Jet magazines and a consensus of newspapers:
* President Reagan signs a bill making the birthday of Martin Luther King Jr. a nationwide holiday beginning Jan. 15, 1986.
* Some 250,000 people march in Washington people to celebrate the 20th anniversary of the civil rights march on Aug. 28, 1963, that was highlighted by Dr. King's ''I have a dream'' address.
* Harold Washington is elected mayor of Chicago and W. Wilson Goode mayor of Philadelphia. Including Tom Bradley of Los Angeles and Coleman Young of Detroit, blacks are mayors of four of the nation's seven cities with populations of more than 1 million.
* Jesse L. Jackson seeks the Democratic Party nomination to run for President.
* Guion Bluford becomes the first black astronaut to make a space flight. (A second black, Ronald McNair, flew aboard a space shuttle mission Feb. 3, 1984.)
* Some 600,000 register to vote, and 8.6 percent more hold office in 1983 than in 1982.
* Robert N.C. Nix is named chief justice of the Pennsylvania Supreme Court, becoming the first black to head a state high tribunal.
* A black woman, Mary Hatwood Futrell, becomes president of the National Education Association (NEA), the nation's largest organization of educators.
* Alice Walker wins a Pulitzer Prize for her novel, ''The Color Purple.''
* Vanessa Williams is crowned Miss America. The first runner-up, Suzette Charles, Miss New Jersey, is also black.
* Michael Jackson becomes the superstar of pop music, selling 23 million copies of one album, ''Thriller,'' and winning numerous pop-music awards.
But ''this is only the frosting,'' Jacob notes. ''Black people have no cake to go with the frosting.
''I can't argue with the facts and figures of success. But my concern is a black America plagued with problems - problems not wiped out by a comeback in American industry, not relieved by a lower unemployment rate, not reduced by falling inflation, not eased by the revival of new but expensive housing.''
Jacob raises his voice as he recommends ''priorities'' for 1984:
* ''Get black people back to work!''
* Educate black youth. ''Generate scholastic equity through excellence and high expectancy, in addition to discipline.''
* Upgrade black communities. ''Face up to the problems blacks face - teen-age parenthood, low health standards, inadequate child care, and poor housing.''
* Enforce civil rights legislation. ''Federal policies appear to be designed to wipe out the civil rights gains of the '60s - affirmative action, desegregated schools, equal opportunity.''
* Register and vote. ''The Urban League is a social agency, not a political one, but 1984 is a presidential election year, and the ballot is black people's most potent weapon.''
Jacob says he doesn't expect the federal government to ''look out for us.'' When he took over the National Urban League two years ago, the league received 73 percent of its income from government projects. Not so today.
The National Urban League has received a William Stewart Mott Foundation grant to tackle a ''most troubling problem - teen-age pregnancy,'' he notes. ''More black children are living with single parents than with married couples. As one of our new allies, the Mott Foundation has made a six-year commitment to study this problem.''
Black female heads of households face serious roadblocks - 59 percent have not completed high school; 65 percent have never been married or are divorced or separated; only 41 percent are employed; their median income is only $7,425 (below the poverty level); and they are more likely to be victims of crime, notes ''The State of Black America 1984.''
Although black unemployment dropped from 20.6 percent in December to 17.8 percent in January, it remains twice the national rate and only moves blacks ''from depression to recession,'' Jacob says. The figures? Two million unemployed, 1.4 million ''giving up'' the job search, 500,000 working part-time but hoping for full-time positions, and 49 percent teen-age unemployment.
One-third of black families live at or below the poverty level, he says, including more than half of the nation's black children, and 75 percent of households headed by black women.
The high-technology revolution offers only ''limited growth'' for blacks in the job market, says ''The State of Black America 1984.'' It encourages black youth to complete training in this field.
As Urban League president, Jacob is administrator, fund raiser, and program designer. ''Our goal is to close the widening gap between white and black Americans - in economics, in education, in social justice,'' he says.
Many whites think blacks want ''too much,'' says Jacob. ''This is a short-sighted view. Equal opportunity for blacks is new - coming since 1954, when racial segregation in public schools was termed illegal. And most of our rights came in the '60s, when we hit the streets.
''We still want parity. We want in - to share what this nation has to offer. This is what America is all about!''