It is a little hard to imagine an unemployed black Chicagoan digging out on a cold November morning to go to the polls to vote for Adlai Stevenson II, who is not exactly a "soul" candidate for the governorship of Illinois.

Hard, but not, according to his hopeful handlers, impossible.

"If they were motivated enough to come out and register," says Stevenson's manager, Joe Novak, "they'll be motivated enough to come out and vote."

The new black registration figures are just in from Illinois and are stunning. In one day, a drive called "Come Alive on Oct. 5" added 137,000 names to the rolls. This followed on the heels of various other efforts, which Stevenson helped finance, that brought in 102,000. Of these striking numbers, 60 percent were new black voters.

Black voters are not enamored of Stevenson, who is wooden on the stump and, in the midst of a hapless campaign, felt it necessary to stand up and say, "I am not a wimp." Nor are they particularly mad at incumbent James R. Thompson, a dashing and resourceful campaigner who has largely managed to overcome disabilities that fall upon a man who tried to appoint his wife to the state bench and accepted lavish presents.

Stevenson's memberships in two clubs that bar women were an issue until he resigned from them. But in the end, it's the party, not the clubs he belonged to, that he hopes will make the difference, particularly with black voters.

The election offers them their first chance to get even with President Reagan, who has put them out of work, shredded welfare programs, dragged his feet on extension of the Voting Rights Act and generally given blacks a powerful impression that he is not on their side.

Reinforcing that impression this week, the administration is going before the Supreme Court to argue that the Internal Revenue Service does not have the right to withhold tax exemptions from Bob Jones University, a segregated institution.

"Blacks hate Reagan with a vengeance," pollster Peter Hart says. "There is nothing of comparable intensity in survey data."

What Hart calls a "blacklash" could be an important factor in gubernatorial races in the two largest states, California and New York.

Thompson, who is ahead in the polls, has courted blacks, won the backing of several black politicians and been endorsed by the Chicago Defender newspaper. But unemployment for blacks runs at 20 percent and for black teen-agers at 60 percent. If blacks turn out Nov. 2 and run true to form--that is, Democratic--Stevenson will receive, at a minimum, 65 percent of their vote. The theory is that if he comes out of Chicago with an edge provided by black voters, he could neutralize Thompson's downstate strength.

The Democratic National Committee, aware, as one staff member put it, that black voters could put "some passion, some electricity into the process," formed a voter registration and participation division, to galvanize black voters. They have produced a series of election day "pulling" commercials, in which prominent black politicians urge their brothers and sisters to get to the polling places as if their lives depended on it.

In New York, black voters have already used Mayor Edward I. Koch as a surrogate punching bag for Reagan. Democrat Koch was cozy with the president, preached austerity and closed down facilities in minority areas.

Koch's Democratic rival, Lt. Gov. Mario Cuomo, pushed a registration drive. The turnout in the black wards, always low in a primary, increased to 40 percent and helped hold Koch's margin over Cuomo down to one-half of one percent in New York City. Cuomo, now facing Republican Lewis Lehrman who is more Reagan than Reagan, is not fearing black apathy on Election Day.

In California, 630,000 new voters, including 200,000 blacks, have been added to the rolls. The blacks may well be the most motivated voting bloc in the electorate Nov. 2. Not only do they get a chance to paste Reagan, but they also get the chance to elect Tom Bradley the nation's first black governor since Reconstruction.

Los Angeles Mayor Bradley, a calm and imposing figure, is counting, of course, on white votes because blacks comprise only 8 percent of California's voters. But the race has taken on a new cast. Bill Roberts, campaign manager for Bradley's Republican opponent, state Attorney General George Deukmejian, injected the race issue by suggesting that a hidden anti-black vote would eventually sink Bradley.

Deukmejian denied charges of racism, but Bradley called attention to the "slur" on the intelligence of California voters who, he said, will make their judgment on merit.

Democratic National Committee Deputy Chairman Ron Brown concedes that half of the nation's blacks eligible to vote are still not registered. But those who are, he thinks, will appear on Election Day.

"They see they have made a difference," he says. "And they'll want to get out there and do it again."