Jackie Cowsky is a Bridgeport Democrat, and for all 47 years of her life, that has meant Democrat to the core in city politics.

From 1933 to 1979, every mayor of Chicago was a resident of Bridgeport, a blue-collar ethnic enclave on the southwest side where the Daley & Daley insurance agency has its office, where Cook County State's Attorney Richard M. Daley grew up, where John P. Daley is the Democratic ward boss.

In 1979, Cowsky broke one tradition by sticking with another. She reluctantly voted for the party nominee for mayor: Jane M. Byrne from the northwest side. The spunky Byrne won, and after four years in office her name became a household curse among many Bridgeport Democrats.

Now Byrne is headed out of office, a loser for renomination in the Democratic Party primary, as was Cowsky's favorite, Richard Daley.

That leaves Cowsky and thousands of rock-ribbed Democrats in race-conscious neighborhoods with a choice in the April 12 general election of staying the party course and giving Chicago its first black mayor or voting for a white man who would become the first Republican mayor since 1931.

"The big thing about this election," Cowsky said, "is there's lots of talk about it's not racial. It's racial. A lot of your white people don't want a colored guy in, and a lot of your white people are going to vote Republican. I'll make you a dollar bet."

She rested her chin on the clothes rack and stared down the long row of toddler and infant wear at the Family Discount Store on Halsted Street where she works and where more and more of the customers are black.

The Democratic nominee, U.S. Rep. Harold Washington, "would probably do a good job," she said. But, she adds, "it all boils down to the color of his skin, and if they tell you 'No,' tell them they're a damn lie."

As the race for mayor enters its final two weeks, the legacy of decades of poor race relations in some of Chicago's staunchest Democratic neighborhoods is jeopardizing the party's monopoly on City Hall, on the national Democratic Party's credibility with blacks and on the reputation of America's second-largest city.

Washington, 60, won the nomination Feb. 22 after blacks had registered and turned out in unprecedented numbers and most white votes were split between his two white rivals, Byrne and Daley. Last week, he picked up the endorsement of the local Democratic machine, the 50-member Cook County Democratic Central Committee.

Yet Washington is hardly assured of victory April 12, especially since Byrne abandoned her write-in campaign and made it a two-way race.

Last week, Republican Bernard E. Epton, who received all 11,000 votes cast in the Republican primary, said he thought the race was nearly even. Al Raby, Washington's campaign manager, said Friday, "It's clear that we can win, but it's not an easy victory."

Six of the 50 Democratic ward committeemen--the party bosses--have endorsed Epton and others are expected either to follow suit or remain officially neutral while working for him behind the scenes.

They said they would rather take their chances with a Republican mayor than a maverick Democrat who campaigned against their patronage system and vowed to eliminate it if elected.

Yet among some voters interviewed at a candidates' forum in Marquette Park and in the stores along Bridgeport's main street on a windy spring afternoon last week, the issues are more personal, more basic and sometimes more difficult to voice.

"I don't know how to say this," said Perry Zatarski, a truck driver from Marquette Park, "but most people are afraid that he Washington is going to exert all of his powers for the black community and the white community is going to get nothing."

"My fear," continued Zatarski, who said he voted for Daley in the primary, "is that he's going to try to push racial integration, which is fine as long as I don't lose money on my house when I decide to sell, because I can't take the loss."

Zatarski's wife, Renee, said she is afraid Washington will put all of his emphasis on helping the poor, not struggling middle-class people like her family. "I just see in the newspapers that the black community gets the impression that they are the only ones hurting in these times," she said. "Everybody is hurting."

The Rev. Robert S. Moore, a Methodist minister, recalled one elderly parishioner telling him, "If that black man gets elected, no white woman would be safe on the streets. The blacks will just take over."

"It doesn't do any good to say it's racism. But it runs deep," said Moore, pastor of the Elsdon United Methodist Church in nearby West Gage Park and president of the Southwest Community Congress, which sponsored the candidates' forum.

Transition is occurring slowly in this area, as it is in Bridgeport not far away.

"It's the toughest decision I've faced, to vote for a black man," said Bridgeport resident Michael Kozicicki, a city water reservoir employe who said he got his job through patronage 11 years ago. "I'm not going to lie to you. I don't want to see trouble in this city."

The uncertainty in these predominantly white wards is reversed in black neighborhoods, where Washington's campaign remains a crusade.

Just before his appearance in Marquette Park, Washington spoke to a crowd at the St. John Temple Baptist Church on the South Side.

For nearly half an hour, he preached a gospel of political empowerment and accountability, promising to include people like the leaders of the anti-poverty group that helped organize the rally, The Woodlawn Organization, in government if elected, and defending the virtues of ethnic politics.

When Irish Catholics exulted at John F. Kennedy's 1960 election as president, Washington said, "We didn't ask the Irish Catholics for an explanation. We just knew they wanted one of their own to reach the top.

"We try to push one of our own and everybody asks us for explanations. 'Aren't you happy?' 'Why would you push one of your own?' 'Are you racist or something?' "

"Any politician will stress his base. Is there anything wrong with a black base? "

Washington's racial overtures irk many white Chicagoans. They complain that whenever they criticize him, don't appeal for the black votes they feel he already has, or just say that they prefer another candidate, they are painted as being racist.

"I've voted in every election since I was 18," said Renee Zatarsky. "If I'm white and I choose to vote for Epton or I choose to vote for Jane Byrne does that mean I'm wrong? "

Rounding up white votes from strongly Democratic areas will be difficult for Washington. To win, his strategists estimate he would need 600,000 votes from minorities, mostly blacks, and 80,000 to 100,000 or more from whites. Chicago politics are often negative. Many of those who supported Daley in the primary, for instance, said they did so primarily to defeat Mayor Byrne. And with Byrne out of race, observers said, Washington could emerge as the candidate some might want to vote against.

Epton, moreover, has emphasized that he intends to be mayor for no more than one term, a four-year reign palatable to disgruntled white Democrats choosing the lesser of two evils.

Washington has made numerous gestures of reconciliation. He has toned down criticism of the police department, emphasized at nearly every stop that he considers himself good at building coalitions, and hinted that he could be flexible on party patronage.

But such gestures are not enough for one of his critics, Alderman Roman C. Pucinski, who officially is still neutral.

"There are 1 1/2 million votes in this city," Pucinski said, "One-third of them are black, two-thirds of them are white. If they want to kiss off the white votes, that's their business. But then let them pay the consequences, not us."

Washington also has talked to disgruntled ward bosses from the northwest and southwest sides, ethnic neighborhoods where opposition to him is greatest, and he is making campaign appearances in white neighborhoods.

Perry Zatarski said he felt more like he could vote for Washington after hearing him speak at the candidates' forum, but he said he still wasn't sure. And he and his wife were the only ones from their block to attend the forum, he said.

Bridgeport Democrat Jackie Cowsky already has been given an Epton-for-mayor sign, and Epton has opened a headquarters on Halsted Street in the heart of Bridgeport, something that no serious Republican candidate would have dared do a few years ago. Cowsky has not put up the sign.

"It's sitting there on the coffee table. I'm not going to put it up. I'm going to put it in the garbage can," she said, adding, "I could have a Washington sign and I'd say I'd put it in the garbage can, too."