Anyone who anoints himself leader of an organization called People United to Save Humanity thinks spaciously, and Jesse Jackson, founder of PUSH, is thinking of entering the Democratic presidential primaries.

He probably would get only a small sliver of even the black vote. Being frivolous with the franchise is a luxury of the comfortable. Besides, Jackson's complaint against the Democratic Party is, to say no more, unconvincing. It is that the party holds blacks "in contempt." Actually, it has promised much to blacks, it has kept its promises and, given the parlous state of the republic's budget, there is not much more, aside from "affirmative action," it can promise at the moment.

A Jackson candidacy would be unserios. But the untapped strength of the black electorate is serious and, for Republicans, ominous.

Winning reelection in 1982 as Pennsylvania's governor, Richard Thornburgh got 20 percent of the black vote, about double what most GOP candidates got nationwide. But in 1978 he got more than 50 percent.

True, in 1978 he was helped by the Democratic Party's entanglement with Frank Rizzo, Philadelphia's polarizing mayor. But in 1982 Thornburgh was endorsed by many state and national black leaders (including Jesse Jackson), yet could not counter the bitter, galvanizing hostility blacks feel for Reagan's policies and for Reagan personally. This bitterness may be the most underestimated force in U.S. politics today. Reagan is becoming the fourth factor in transforming the black electorate into a formidable anti-Republican sword.

A paper prepared by the Joint Center for Political Studies, a black research organization, notes that three events turned blacks into the Democratic Party's most cohesive bloc. One was the relief provided by the New Deal. Another was Harry Truman's civil rights legislation and 1948 civil rights plank that provoked Strom Thurmond's Dixiecrat candidacy. The third was the Republicans' nomination in 1964 of a candidate, Barry Goldwater, opposed to the 1964 Civil Rights Act.

Today, the paper says, "not only are the black poor dependent on government transfer programs; the black middle class is also heavily reliant on the public sector for employment opportunities and contracting arrangements." This limits the extent to which the GOP can appeal to blacks even if it invigorates the private sector.

In 1956 Adlai Stevenson got only 61 percent of the black vote, and four years later John F. Kennedy got only 68 percent. But since the civil rights revolution, the Democrats' share (according to Gallup) has been: 1968--85 percent, 1972--87 percent, 1976--85 percent, 1980--86 percent.

True, Jimmy Carter got all but 14 percent of the black vote and lost all but six states. But momentous consequences can flow from changes at the margin in democracy. Of the 17 million blacks of voting age, only 10 million are registered and only 7 million voted in 1982. If 11 million voted, that would mean at least 3.5 million more Democratic votes.

In 1969 there were 1,160 black elected officials. Last year there were 5,160. But that is just 1 percent of all elective offices. Aside from two Mississippians elected during Reconstruction, Ed Brooke (R-Mass.) is the only black to serve in the Senate (1969- 79). Only 52 blacks have served in the House, about half during Reconstruction; most--21--of the blacks elected in this century are now in Congress.

Only 14 congressional districts (three in Chicago) have black majorities. But blacks comprise at least 20 percent of the population in 86 districts that may be decisive in the Democratic primaries. Only 26 are northern urban districts. The other 60 are in the South.

Fifty-three percent of all blacks live in the South. But in four of the five states with the most electoral votes (California, New York, Texas, Illinois--a total of 136 electoral votes, more than half of the 270 needed to win), there are more than 1 million black voters. Twenty-eight of the nation's largest cities have more than 100,000 blacks. Thirty cities with more than 30,000 residents have black mayors. In 24 of the 25 largest school systems, a majority of the students are black or other racial minorities.

No candidate since Dwight Eisenhower in 1952 has won the presidency without carrying at least three of these six northern industrial states: Illinois, Michigan, New Jersey, New York, Ohio, Pennsylvania. In these states there are approximately 5.5 million blacks of voting age--a lot of them hitherto unregistered.

Republicans who are not dismayed by these numbers do not understand the political potential of the black vote, or the social failure represented by the fact that 11 percent of the electorate is essentially inaccessible to one party.