New York — New Jersey's primary next Tuesday is called ''crucial'' for the three Democratic contenders. For Walter F. Mondale, it would show continued strength in large Eastern seaboard states and could soften a potential loss in California. A victory for Gary Hart would continue his resurgence begun in Ohio and Indiana. And the Rev. Jesse Jackson could gain more delegates to consolidate his bargaining power at this July's Democratic National Convention.
But after the campaign dust has settled, and the mobs of reporters wearing identification tags around their necks have left, where will New Jersey politics be?
A contested primary is new to the state, observers say. And the political fallout from this year's lively match may affect future races, including next year's gubernatorial campaign.
Republican Gov. Thomas H. Kean is popular, New Jersey Democrats admit, and no one is predicting he can be easily defeated. But as Mr. Mondale, Senator Hart, and Mr. Jackson hit hard on the topics of waste disposal and toxic pollution, more and more voters link the Republican Party with inaction on such issues.
''The Reagan administration is not environmentally sensitive,'' says Democratic US Rep. James J. Florio, who is considering a gubernatorial run next year. He says New Jersey voters make that connection. Their state has the largest number of sites on the federal Superfund priority list of toxic waste dumps.
He also points out that whoever is elected president will have to deal quickly with the large budget deficit. With rumors that the Reagan administration plans ''substantial consumer-oriented'' tax increases, the incumbent governor could find Reagan policies a giant albatross, says Mr. Florio , even though Governor Kean has tried to separate himself from the President on such issues as the environment and civil rights.
''A lot depends on the outcome of the election in November, particularly in New Jersey,'' says Florio. The state has carried GOP presidential candidates since 1964. ''I think we can change that.''
Albert Burnstein, a former Democratic state assemblyman, says chances for a Democratic gubernatorial victory next year are very slim, but he adds that elections are very volatile. A change in the national economy could hurt Kean, as it did US Rep. Millicent Fenwick in 1982, when she was defeated in her try for the US Senate by businessman Frank Lautenberg.
One potential side effect of the race, says Mr. Burnstein, will be a more clear-cut division between Democrats who are ''future'' oriented, a la Gary Hart , and those who are more ''establishment.'' He says this election may be a prototype for the governor's race next year, in which up to four or five Democrats may vie to run against Kean. Besides Florio, names mentioned include Newark Mayor Kenneth Gibson; Alan Karcher, speaker of the state's lower house; Peter Shapiro, a country executive; and former Assemblyman Stephen Wiley.
Clarence Coggins, state coordinator for Jesse Jackson, says that as in other states, the Jackson candidacy focuses on bringing in ''locked out'' voters. And although minority representation in New Jersey is already well established - there are black mayors in such major cities as Newark and Camden - this campaign will make the black political machine ''more mature,'' Mr. Coggins says.
He also mentions the gubernatorial race.
''We will be better organized,'' he says. ''And we will have educated the voter.'' He says that by next Tuesday, grass-roots workers will have contacted 170,000 potential voters, ''eyeball to eyeball.''
The candidates are following rather than leading on environmental issues, says Cliff Zukin of the Eagleton Institute of Politics at Rutgers University. He points to a poll by Eagleton showing that New Jersey voters are more concerned about toxic waste and air and water pollution than about pocketbook issues.
Burnstein and other political observers say the candidates' talk about job retraining and high technology is a bit ''amorphous.'' Employment in New Jersey, with almost 60 percent of its workers white collar and an unemployment rate under 7 percent, is not a hot issue, says Mr. Zukin.
And the peace issues, which cover everything from foreign affairs to the nuclear freeze, is more ''stylistic,'' he adds.
''No one is for nuclear war in New Jersey. The question is how convincing you are'' on the issue of peace.
Zukin says Hart's gaffe over where he and his wife are campaigning (''The good news for her is that she campaigns in California and I campaign in New Jersey'') may be a smoldering issue for the candidate. Hart says the statement was not intended as a slight to New Jersey, but a comment on commuting back and forth.
''In the last few years there has been a beginning of development of state pride,'' says Zukin. ''(New Jerseyans) are tired of having jokes made about their state.'' He says most voters will agree that Gary Hart doesn't actually dislike the state. But it is a sensitive issue - and in a close race, Gary Hart can't afford a defensive campaign.