Harold Washington's hairbreadth victory in Tuesday's Chicago mayoral race provided something for everyone in national politics.

It gave the Democrats a new national figure, whose ability to enlist a massive turnout of black voters seems certain to provide fresh impetus for a 1984 national mobilization of minorities strongly opposed to President Reagan and the Republican Party.

It gave Republicans an opening to thousands of traditionally Democratic, ethnic white Catholic Chicago voters, who supported Washington's opponent, Bernard E. Epton. Some Reagan strategists think those voters will help Reagan carry the key state of Illinois next year, and their counterparts may help him elsewhere.

It gave blacks contemplating the possibility of running a black candidate in next year's Democratic presidential primaries an object lesson in the potential of such a candidacy--but left black leaders sharply divided on the wisdom of such a tactic.

The least complicated reaction was that of national Democratic leaders, who, in the words of party Chairman Charles T. Manatt, "join in celebrating Harold Washington's victory" as an event that "will not be good news for Ronald Reagan and the Republicans."

To them, it means continued Democratic control of a City Hall machine that has contributed significantly to every Democratic presidential victory since Franklin D. Roosevelt's first election.

The Democratic National Committee put about $90,000 in cash and services into Washington's race--unprecedented for a local contest--and helped arrange a series of endorsement appearances by big-name Democrats.

Aside from Washington's winning, the best news for the Democrats was the record-breaking registration and turnout of black voters that was spurred by his candidacy.

Atlanta Mayor Andrew Young (D) said yesterday that the changed turnout arithmetic "will revise strategies for victory, as Democratic candidates come to understand its meaning. In a national election, an 80 percent turnout of voters--of any color--would assure a Democratic victory."

The leading Democratic presidential candidates shared that view. At a news conference in Birmingham, Walter F. Mondale said Washington's victory will help Democrats be "seen as a party that's concerned about all Americans and a party that will not exclude some people . . . . We want to be a party . . . in which racial and religious distinctions are less important in terms of public policy."

Mondale drew Washington's ire by endorsing State's Attorney Richard M. Daley in the Chicago Democratic primary, but was at the new mayor's side during one of the ugliest incidents of the general election campaign, when hecklers assailed both of them outside a Roman Catholic church in a white neighborhood.

Sen. Alan Cranston (D-Calif.), the only presidential contender to endorse Washington before the primary, said he was happy that "a majority of the voters" had agreed with his judgment.

Manatt, in his statement, said, "The blame for the racial polarization that marred this campaign rests with the Republican Party. They saw an opportunity and seized on the chance to exploit racial politics."

His opposite number, Republican National Chairman Frank J. Fahrenkopf Jr., replied that he was "astonished" that Manatt would "in any way imply the Republican Party or its candidate was guilty of injecting racism into this campaign . . . . The issue of race was raised for the first time by Democrats in the Democratic primary."

The Republican National Committee put about $65,000 worth of services behind Epton.

White House spokesman Larry Speakes declined to comment on the election.

Some Republican strategists said they think the rift in the Chicago Democratic organization displayed by the desertion of Washington by many white ward leaders will play into the GOP's hands in 1984.

Both Lyn Nofziger, former head of the White House political office, and Robert Teeter, a leading GOP pollster, said the votes Epton gained from traditionally Democratic whites might stay Republican in 1984.

"However tough it was the first time," Teeter said, "it will be easier the second."

A third Republican strategist, close to Reagan, called the election a "no-lose" situation for the GOP, and said, "it's probably slightly better for us" that Washington won--on the assumption that he will continue to polarize the Democratic organization and electorate along racial lines.

"Democrats need two-thirds of the city vote to carry Illinois," he said, "and Washington will have a whale of a time delivering more than the 52 percent he got yesterday."

Among black Democrats, the celebration of Washington's victory and the high black vote turnout that made it possible turned quickly into a consideration of strategies for 1984.

The Rev. Jesse Jackson, the Chicago-based civil rights leader who has been the most outspoken advocate of a black candidate entering the 1984 presidential primaries, called the Washington vote turnout "the most significant national event--especially for mobilizing black youth--since the Selma-to-Montgomery march. Now they know they can stage a political confrontation, with enough numbers to win."

Gary, Ind., Mayor Richard G. Hatcher and Rep. Mickey Leland (D-Tex.), both influential members of the Democratic National Committee, endorsed that view.

Leland said the high turnout of blacks "provides further impetus" for a black candidacy. Hatcher said that "it will enhance the possibility of a serious black candidate."

"When you think about the power the mayor of Chicago has," Hatcher said, "he could by his involvement make a bigger contribution than anyone else."

National Urban Coalition President M. Carl Holman, who had been skeptical of the idea of a black running for president, said he was becoming an advocate.

"Nothing turns out black voters like a black candidate," he said, adding, "A black candidate can reach out and bring along with him people from the peace movement, Hispanics and women."

Like the others, Eddie N. Williams, head of the Joint Center for Political Studies, said the Washington victory "will result in increased black political mobilization around the country for 1984. It's amazing how much hope was riding on this."

But Williams also said he thinks "Harold's victory defuses to a slight degree the intensity of having a black candidate."

Andrew Young, who has opposed the black candidacy idea, said, "It will probably stay alive for awhile, because Jesse Jackson , with some justification, can claim it the Washington victory as a credit for his aggressive style of politics." But he said that personally he is still not persuaded.

Joseph L. Reed, chairman of the Alabama black Democratic Conference and another skeptic, said the Chicago election "won't be the controlling factor" in the question of a black candidacy. "We'll have to assess what it means and to what extent a black candidate might hurt a white who is sensitive to black needs."