Republicans have won four of the last five presidential elections. They win plenty of statewide races, but they hold only 41 percent of House seats and 39 percent of the seats in state legislatures. A clear pattern: Republicans have strong stars but a weak bench. Can that change? A test comes Tuesday in New Jersey.

There the incumbent Republican governor, Thomas H. Kean, led Democrat Peter Shapiro 67 to 16 percent in an October poll. Meanwhile, his Republicans are trying to overturn the Democrats' 43-37 margin in the assembly.

One of the people trying to help bring it off is Jack Rafferty. Tall, silver-haired, with an unlined face at 47, Rafferty has the hearty handshake of a man who has been mayor of Hamilton township for 10 years. It's a big job: historically Democratic, mixed blue-and white-collar, Hamilton has 87,000 people, almost as many as next-door Trenton, and Rafferty got voters to approve a strong- mayor system and a $52,000 salary.

Rafferty was raised as a Democrat and an Irish Catholic; his parents worked polls for Democrats. But when a friend prodded him to run for council 16 years ago it was as a Republican -- "no great philosophical switch," he says. Now he is the Republicans' best hope to win one of the two Assembly seats in the 14th district, which was 50-50 in the 1981 governor's race, a race Kean won statewide by 1,797 votes. Rafferty's work on community rehabilitation and new development makes him popular in Hamilton, and he campaigns elsewhere as a Kean backer.

The stronger Democrat in the 14th is Joseph Bocchini, 41. His pinstriped suit askew, he flicks ashes on the marble floor as he argues before State House reporters that his subcommittee has power to issue a subpoena to Price Waterhouse to look into a contract it has with the state. This is part of the Democrats' strategy: they say they help Kean when he's right but are watchdogs when needed. (Kean disarmingly admits the contract was "screwed up" and says it will be fixed.) Bocchini is raising most of his own money and running on his own local accomplishments (an EPA loan for East Windsor to dredge a lake); he attacks his Hamilton neighbor, Rafferty, because he says he plans to continue as mayor and collect two salaries if he wins.

Both Rafferty and Bocchini light up over the gritty details of local government. No government-is-the-enemy talk here: both assume government can and should solve problems. As Bruce Benedetti, a former Democrat who is in charge of spending $1.2 million as director of Republican Majority '85, goes over 15 targeted districts, he recites one local angle after another. One incumbent has high absenteeism; another couldn't get his toxic waste bill on the floor; a third has failed to win a chairmanship. Challengers have this or that local advantage. Behind his desk in a Trenton rowhouse are charts showing when "radio/print wave 2" is to begin. The mailings and radio ads for each district are prepared by Benedetti's group and only then approved by the candidates: the issues are local, but the campaign is centralized and well organized.

In his wood-paneled office in the old State House, below the picture of Woodrow Wilson, Tom Kean makes it clear this didn't happen by accident. "The legislators have tried to make themselves into little congressmen, with staff, phones and mailing privileges, and so you don't have the kind of coattail effect." That means you must find strong candidates. "Recruiting was the most important part of the equation, and we've gone in district by district to talk popular people into running."

Kean talks with gusto not only about politics, but about the accomplishments of government: new jobs, a transportation trust fund, a clean-water environmental trust fund, enterprise zones, lowering some taxes. He crackles with enthusiasm on his issues for the next four years: environment, raising teachers' salaries, innovative education programs such as lateral entry for teachers. He is proud that he has reached out to blacks and kept his door open to labor.

Kean benefits from his personality and from the widespread feeling that New Jersey is moving in the right direction, that its economy is shooting ahead, that this backyard state has found an identity. He speaks breezily in a Brahmin accent, and like his favorite 20th century president, Teddy Roosevelt ("a distant cousin of my dad's"), seems genuinely interested in ordinary people and eager to talk with them. His job rating is over 70 percent positive. Shapiro is running ads that start with the white letters "BULL" on a black screen, followed by the candidate saying Kean hasn't cleaned up toxic waste as he claims. It is uphill campaigning, and there is no indication that Kean is hurting.

In the assembly races, both parties' candidates try to associate themselves with Kean's perceived successes and New Jersey's progress, the Democrats as incumbents, the Republicans as backers of Kean. If -- as seems likely -- the Republicans gain a majority, they will have proved mainly that they can come up with enough good candidates in a reasonably typical state. That's an achievement, but not one automatically replicable elsewhere. It requires advanced planning, aggressive fund-raising, centralized control of campaigning, a positive commitment to government, and -- not least -- the instinctive political talents of former Democrats. If New Jersey shows the Republicans can develop a strong bench, it will turn out to be one that looks a lot like the other side's.