This city's mayoral election next Tuesday is the exception to the rule about the national insignificance of local contests. The battle between Rep. Harold Washington, Democrat, and former state representative Bernard E. Epton, Republican, is one that can shape the climate for the 1984 presidential contest as profoundly as any event in this year.

Even if the voting is conducted calmly and the verdict accepted peaceably, there are important consequences for the Republicans and immense ramifications for the Democrats. Consider some of the points made by officials and strategists in both parties.

For the GOP, the pluses are these: whether or not Epton becomes the first Republican mayor in 52 years, his campaign has brought the Republican Party into close alliance with thousands of white, working-class, urban, ethnic Catholic voters--a prime target group for Ronald Reagan's reelection campaign.

If Epton wins, the GOP captures control of one of the real power centers of the Democratic Party, disrupting Democratic hopes for carrying Illinois in 1984. With Epton in City Hall and Republican Gov. James R. Thompson in Springfield, Reagan (or any GOP nominee) would have a leg up in a state that historically has been essential for Republican presidential victories.

The potential GOP liabilities are these: Epton, a liberal Republican, is no Reaganite and, with the attention he would command as the biggest-city GOP mayor, many who know him expect he would be a thorn in the administration's side on urban programs and budget priorities.

Win or lose, the Epton campaign is certain to solidify black opposition to Reagan and other Republicans and to create new doubts in the minds of independents who reject any party or candidate they view as using "racist" tactics. Epton's attacks on Washington's criminal convictions for tax evasion and temporary disbarment for appropriating clients' funds are legitimate. But his campaign slogan, urging voters to support him "before it's too late," has been condemned by the Chicago papers and many others as a racist appeal.

He denies it, but the charge stings him and the nationally established Republican consultant firm of Bailey Deardourff, which created it. Washington and other Democrats have charged that the Reagan White House orchestrated the theme--and to the extent that the racist charge sticks, it is likely to hurt all Republicans.

Epton has promised that as mayor he would bring blacks into major roles in running Chicago. So far, however, the Epton campaign has brought to the surface the one charge Reaganites most fear: that their party and its policies are more than biased toward the wealthy, they are biased against blacks.

But the GOP's worries are minor compared with the Democrats'. Theoretically, Democrats could come out well in Chicago--but only if Washington wins and proves to be a broad-gauged, inclusive and effective mayor, who helps the national party and its 1984 candidates.

But the risks are great that one way or another, the damage to the biracial Democratic coalition that has already occurred here will be increased by the opposite set of events. If Washington loses in this historic Democratic stronghold, no Democrat I know doubts there will be a massive black backlash against the party.

No matter that every Democratic presidential hopeful has campaigned with Washington and the Democratic National Committee has put in unprecedented resources. The failure of many key leaders of the city Democratic organization--and their white Democratic constituencies--to accept a black mayoral nominee will trigger great resentment. Most of those I have talked to think a black candidacy in the 1984 presidential primaries would become inevitable if Washington loses --damaging the chances of Walter F. Mondale and other liberal white candidates, and posing serious problems for ultimate party unity.

"Two years of patching and building from the 1980 defeat can go down the tubes here Tuesday," said one worried national official.

Even if Washington wins, the Democrats may pay a price. Thousands of white ethnics will be left with the bitter feeling that Mondale and others pushed into office a candidate whose personal record would have made these leaders squeamish--were Washington not black. The issue of reverse discrimination, which plagued the Democrats in the '70s on the "quotas" question, and which they thought they had put behind them, would arise in even more emotional form.

Already, some national Democrats talk privately of the "risk" of appearing to be a party too beholden to minorities and special-interest groups. Many of them feel they have gone way out on the limb in vouching for Washington.

If he wins next Tuesday, they will keep fingers crossed to see what happens next. If he loses, a great many Democrats will be saying their prayers.