hen President Reagan came to this suburb the other evening to campaign for New Jersey Republican gubernatorial candidate Thomas H. Kean, he began his speech in an unusual way.

"Let me clear up a misunderstanding that evidently exists with Tom's opponent," Reagan said. "It's not true that I am running for governor of New Jersey. And it's not true that I was going to take the Social Security away from that little old lady on television."

Reagan's opener was a backhanded acknowledgement that "Tom's opponent," Rep. James J. Florio (D), has succeeded to some extent in making the president and his budget policies an issue in the New Jersey race.

The once-desultory campaign has caught fire since Florio began swinging away in both his speeches and television ads at Reaganomics and the derivative version of it he says Kean would "superimpose" on New Jersey if elected.

The result has been to make this election more legitimately a test of public reactions to Reagan's policies than it was last summer when it was first dubbed a "referendum" on Reaganomics.

The irony is that as the national importance of the contest has grown because of Florio's change of tactics, the chances of a Republican upset have increased.

Although Democrats have a big registration edge, the GOP has held the governorship only four of the last 28 years and Florio has led in every published poll, Republicans claim that their private polls the last two weeks have shown Kean narrowly ahead. The Florio camp is closemouthed about its polls, but a knowledgeable Democratic politician said the last poll he had seen showed Florio five percentage points ahead--a margin he called "not safe enough for comfort."

The New Jersey "referendum" concept was born of two factors: Kean, a former speaker of the New Jersey assembly, made the centerpiece of his campaign in both the primary and general election a plan for cutting state corporate and sales taxes to spur job growth--an echo of Reaganomics.

And New Jersey, unlike Virginia, the only other state that will elect a governor in the off-year voting Nov. 3, has been a real two-party battleground. Despite the Democrats' dominance in Trenton, Republican presidential candidates have carried the state in the last four elections. Reagan, who cut deeply into blue-collar Democratic precincts in gaining his 400,000-vote victory, said that "nowhere is the political realignment more apparent than here in New Jersey" because its "working people finally realize that the Republican Party is their party."

Early on, it was the Kean campaign that emphasized Reaganomics, by targeting TV ads against Florio's opposition to the Reagan budget and tax cuts. But in the last two weeks, Florio has forced the Reagan issue to the forefront with classic Democratic attacks against the "hard-hearted" policies of Reagan and Kean.

Talking to a Bergen County labor breakfast, where several of the union leaders readily acknowledged to reporters that they had backed Reagan in 1980 and still thought he was doing what one called "pretty good for an apprentice," Florio called on them to combat "the threat to the well-being of the working people of New Jersey" from the Reagan-Kean policies.

There and at a rally at Kean State College, named for his rival's ancestors, Florio invoked the name of the Rev. Martin Luther King Sr., who had traveled to New Jersey to endorse him, as authority for the statement that there is "a certain meanness" about the Reagan-Kean philosophy, "a cavalier attitude about people . . . that is really scary."

"We are not just electing a governor," he said. "We are telling the nation we reject a philosophy that seems to be prevailing . . . . "

Florio strategists say the head-on challenge has begun to solidify the Democratic vote and has halted the erosion they acknowledge was taking place in Florio's early lead.

Florio said he thought the tactic was keeping Kean on the defensive. "Tom is a thoughtful guy," he said, "who was a moderate in the legislature. He took this Reagan tax position to get through the primary and now he's stuck with it. But he's not comfortable with it."

Republicans tell a different story. They say Florio switched to the national issues only when the polling showed Kean was moving ahead on the major state concerns: the desire for a change from two-term Gov. Brendan T. Byrne (D), who is ineligible to succeed himself; cutting crime and taxes, and bringing jobs. Rather than solidifying Democratic support, they said, Florio's attacks on Reagan have helped Kean regain Republican voters in South Jersey who had been supporting Florio as a hometown boy.

Campaigning in Florio's backyard the other morning, Kean told a Chamber of Commerce group that he would try to get government "off your backs," adding, in a show of Princeton scholarship that baffled many of the businessmen, "You know who first said that? It was Tolstoy, the Russian author Tolstoy."

Later, Kean told a reporter that "running against Ronald Reagan is not the way to be elected governor of New Jersey, not with all the burning issues we have in the state. The issue in this election is not Ronald Reagan. It's Tom Kean and my program. And that's why I'm going to win."

If he does win, however, Reagan has certainly set the stage--with Florio's help--for claiming a share of the victory.