President Carter toured the spiritual heartland of the old Democratic coalition today, preaching against the evils of Republicanism and reminding the black, Catholic and Jewish voters of the Northeast that he, too, is a Democrat.

From a black Baptist church in Newark, N.J., where he made his last campaign stop of Wednesday night, through a huge noontime labor union rally in New York City today, the president did exactly what Ronald Reagan has accused him of doing -- wrapping himself in the mantle of the Democratic Party.

In the process, Carter, as he did in his debate with Reagan, touched many of the key constituent groups in the traditional Democratic alliance in a last-minute push to bring those voters and their heritage of voting for the Democrat to the polls next Tuesday.

To a Polish-American audience in Philadelphia's Pilsudski Club hall this morning, Carter fondly recalled the election of John F. Kennedy, the nation's first Roman Catholic president, and pledged his solidarity with the rebellious workers of Poland.

A short time later, speaking to the Young Men's Hebrew Association in the same city, he denounced religious intolerance and reiterated his support for Israel in the strongest terms he has used in the campaign.

And at the corner of 37th Street and Seventh Avenue in Manhattan, at a rally organized by the International Ladies Garment Workers Union, he declared that New York is "the greatest city on earth" and attacked Reagan's positions on urban aid, the minimum wage and other social welfare issues.

The president stopped here later today and, in a voice growing raspy from the strain, continued his assults on his Republican opponent at a rally before flying to St. Louis for another campaign event.

With the likelihood of a dramatic break in the hostage crisis before Election Day diminishing, traditional political factors such as voter turnout in Democratic strongholds, like Philadephia and New York, are growing in importance to Carter. It has also become increasingly clear as the election nears that the president's chances of remaining in the White House are riding heavily on two fragile strands of loyalty -- those of southerners to him as one of their own, and those of big city northerners to their political heritage as Democrats.

Carter, who ended up tonight in Columbia, S.C., will spend the next two days in his native South talking about his roots, just as he spent today in the North stressing his ties to some of the Democratic giants of the past.

But the signs of enthusiasm that Carter and his advisers are looking for to suggest as big Democratic turnout next week were not always evident as the president campaigned today. Carter has seldom until recently stressed his ties to the Democratic Party or generated much emotion in his audiences, and his efforts to do both now appear to be meeting with only mixed success.

But the president's chances of winning reelection depend heavily on the voters he addressed today turning out next Tuesday at the polls, and so his message was the same everywhere -- he is the Democrat, Reagan is the Republican and some things don't change.

"For five decades, 50 years, the Democrats have fought for the rights of working people," Carter said at the Pilsudski hall. "We enacted the minimum wage over Republican opposition.We enacted unemployment compensation over Republican opposition. We enacted Social Security over Repbulican opposition."

To his Jewish audience in Philadelphia, the president said the United States "stands shoulder to shoulder with Israel against all her enemies" and pledged not to sell bomb racks and other "offensive equipment" to Saudi Arabia for its American-built F15 fighter planes.

The streets of New York's garment district were jammed with thousands of people when Carter reached Manhattan at midday to continue to assult Reagan's foreign policy views, which he called "the overriding issue of this campaign."

"Over the last 20 years we've taken the first long step away from the nuclear precipice," he said. "We must stay on that road until the shadow of a nuclear holocaust is lifted from the people of this earth. On issue after issue the choice is clear and the stakes for our country are very high. This is a tough race. It's going right down to the wire."