Mayor Harold Washington of Chicago is the latest national black figure to endorse the candidacy of William H. Murphy Jr. in Tuesday's Democratic primary for mayor. While a crisis over his own city's bond rating forced Washington to cancel a scheduled appearance at a Murphy fund-raiser here Thursday, he sent word that he supports Murphy's campaign to unseat three-term incumbent William Donald Schaefer.

In doing so, Washington joined several other prominent blacks who have come from around the country to praise Murphy, the first black to make a serious challenge for the top elected position in this city, whose population is 60 percent black.

Earlier, the Rev. Jesse Jackson; Atlanta Mayor Andrew Young; former Atlanta Mayor Maynard Jackson; Georgia State Sen. Julian Bond; Martin Luther King III, the son of Martin Luther King Jr., and Dick Gregory came here to help Murphy's underdog candidacy. One endorsement that eluded Murphy was that of D.C. Mayor Marion Barry. An aide to Barry said the two men discussed Murphy's candidacy in Barry's office several months ago, but that no endorsement followed the meeting.

At the same time, Murphy has traveled the country, looking for support and for money, holding fund-raisers in Washington, Atlanta, New York, Los Angeles and San Francisco.

There is good reason for Murphy to take his campaign outside the boundaries of Baltimore. Most of the city's money is tied up in Schaefer, the incumbent having raised more than $750,000, virtually all of it locally. Beyond that, Murphy has had trouble gaining a consensus for his candidacy in the local black community. Many black politicians have endorsed Schaefer, including the last prominent black to oppose him, George Russell, whom Schaefer defeated in 1971.

So Murphy, who stepped down as a Circuit Court judge after three years on the bench in May to challenge Schaefer, has been forced to take his campaign on the road--and to try to import support.

In a majority-black city where black voters have registered in record numbers this year, Murphy would seem to have an excellent chance to continue the national trend and oust Schaefer. Since the city's registration is 10 Democrats for every Republican, their primary is in reality the election. (The winner will face minor Republican opposition in November.)

But going into the campaign's final weekend, local polls show Murphy trailing Schaefer by an overwhelming margin. (A poll in Thursday's News-American had Schaefer ahead 78 to 8.) Murphy scoffs at the polling data. "We're going to win," he said. "At worst this race is too close to call."

Murphy has said all along that he does not want race to be an issue in this election, and there has been no name-calling, none of the heat of last summer's bitter state's attorney's race in which Kurt L. Schmoke, who is black, crushed William Swisher, a white incumbent. But to say the battle lines of the campaign have not been drawn along racial lines is naive.

"Unfortunately, I think both communities will vote along racial lines," Murphy said. "I think the whites will vote for the white candidate, I'll get 10, maybe 15 percent of that vote, tops. That means I'll need 75 percent of the black vote and I think I can get it. The black community is tired of not having meaningful representation."

Schmoke's 2-to-1 victory over Swisher, along with an emerging feeling that Baltimore, like many cities across the country, was ready for a black mayor, led Murphy into this race.

At 40, Murphy's only previous campaign was three years ago when he was elected a Circuit Court judge. On the bench he was known as a defendant-oriented judge who was sometimes criticized for lack of organization--his cases were backed up so far the day he resigned that he was still hearing a case 15 minutes before he was scheduled to announce for mayor.

Since becoming a candidate, Murphy has struggled. Two weeks ago the Internal Revenue Service slapped a $242,000 lien against him for allegedly failing to pay federal income taxes, and a string of financial problems dating back 10 years recently became public. Murphy insists that the publicity about his problems in the Baltimore media--designed, he says, to help Schaefer--will help him. "They went too far," he said. "They've stirred people up."

As he stood in shirt sleeves waiting to make his entrance to a small Washington fund-raiser recently, Murphy insisted that those who predict his defeat do not know what they are talking about.

"William Donald Schaefer is a traditional white mayor," Murphy said. "He grew up in an era when racism was an accepted value. Now, reluctantly, he has tried to make marginal adjustments for blacks and women. He has reluctantly brought a few blacks and women into his administration. But for the most part, those with power in Baltimore are white and male. Those without it are black and female.

"Schaefer has been a good mayor in many ways, but now it's time for a new direction. He's been a great bricks-and-mortar man. He's given the city its first positive ego in 40 years. The image of a city on the move is good, very good. But he missed his opportunity. He could have involved more blacks in the contracting, in the jobs, in everything. He didn't.

"I come from the group that has most of the problems. I understand them. The black community is tired of nonrepresentation. It's been 200 years. They think it's time for a change . . . "

While Murphy depicts himself as "a kid from the projects," he is the son of a lawyer and a member of one of the city's most prominent black families, which founded and publishes the Baltimore Afro-American, one of the nation's most respected black newspapers. Murphy has an engineering degree from M.I.T. and a law degree from the University of Maryland.

Yet he denies a middle-class upbringing the way some people deny being afraid of heights. "When my father built our house in 1946 we had dirt floors and chickens running around," he said. "That house has been upgraded since then, but my parents still live in the very same place."

Murphy is a slender man with curly hair retreating from his forehead and a full beard slightly flecked with gray. His voice is high-pitched and his smile is quick and easy, revealing a pronounced overbite and gaps in his teeth. He is a man who can disarm with words, whose answer to a question may go on for 20 minutes and include much of his life story.

Supporters say he will represent the entire city, not just part of it. Detractors, some of them other blacks in Baltimore, call him an opportunist hoping to take advantage of the trend that has elected black mayors in Detroit, Atlanta, Chicago and, very likely, Philadelphia.

He and Schaefer have dueled all summer over Schaefer's concern, or lack of it, for the black community. Murphy contends that blacks have no voice and no power in the city; Schaefer answers that both have improved considerably during his administration. Murphy says Schaefer's 12 years have benefited the white middle and upper classes and left out low-income blacks. Schaefer says not so. Each cites his own statistics to prove his point.

Those who have come to Baltimore to praise Murphy have repeated his themes and have repeatedly pointed to the jobs done by black mayors around the country.

But only recently has his campaign chest been large enough to begin television commercials. At one point, his campaign was actually in debt. It is difficult enough to beat any incumbent, much less one as popular as Schaefer, without a huge influx of money.

"That's why we've been around the country, because most of the big money in Baltimore is with Schaefer as you would expect," Murphy said. "That's the kind of thing we need to begin changing in Baltimore. We need to start spreading the power and the wealth out. Schaefer hasn't done that. I will."

Murphy's campaign theme is "Time for a Change." But several times, at forums, Murphy has been asked the same question: "Why fix what ain't broke?" as one man put it. Murphy insists much of Baltimore needs fixing. Selling that concept up until now has not been easy. And, with Schaefer due for one final media blitz this weekend, getting it across between now and Tuesday will be very difficult. Yet, Murphy is almost doggedly upbeat.

"I didn't run to lose, I'm not here because I expect to lose," he said as his troubles were cited. Then he smiled and said, "Talk to me Tuesday."