Looking for clues about the future of the Republican Party in the South? Forget for a moment Sen. Jesse Helms (R-N.C.), the guru of the New Right. Consider instead North Carolina's new governor, James G. Martin.

The tuba-playing former chemistry professor is riding a wave of bipartisan good will that eluded Helms in his three successful bids for office.

Even Democrats and "liberal" newspapers, which Helms has made a career of attacking, are heaping praise on the new governor, the second Republican elected to that office in this century.

The Raleigh News & Observer has called him "sure-footed." The Greensboro News & Record said he "is off to a good start in an era of good feeling." The Charlotte Observer editorialized: "If you were writing a script for making a Republican governor acceptable to the Democrat-dominated N.C. Legislature, you could hardly improve on the tactics Gov. Jim Martin is using."

"The new governor is very intelligent, and he is good on his feet. He has to get high marks for his appointments," said Lt. Gov. Robert Jordan, a Democrat.

Martin, swept into office with President Reagan's landslide victory, seems to have pleased almost everyone since the election.

He has courted blacks, women and conservative Democrats (Martin calls them "closet Republicans") while presiding over an uneasy truce between sometimes-warring factions of his party. He has pleased bureaucrats by rejecting wholesale firings. He has pleased the press by opening state meetings, holding weekly news conferences and being generally accessible.

Several well-known Democrats have been given top posts in his administration. Former lieutenant governor Jimmy Green, a Democrat who ran unsuccessfully for his party's gubernatorial nomination last year, has been hired as a lobbying consultant.

Martin, 49, has appointed two blacks to his personal staff and one black -- Corrections Commissioner Aaron B. Johnson, a former civil rights activist -- to his Cabinet. He also attended a ceremony marking the birthday of the Rev. Martin Luther King Jr. -- a highly symbolic act in North Carolina, where Helms made much of his opposition to King's birthday being designated a national holiday.

But perhaps Martin's biggest accomplishment has been to bring a new tone to North Carolina politics. His style is looser and more informal than that of his Democratic predecessor, James B. Hunt Jr., who tried unsuccessfully to unseat Helms last fall.

The Helms-Hunt contest was the meanest, most expensive Senate race in the nation and dominated the state for more than a year. Martin's low-key, somewhat bland manner seems just the tonic the state needed.

Jordan, the titular head of the Democratic Party in the state, said Martin "is not one in the Helms mold. He is more a straight, business-oriented Republican. But his voting record in Congress was very conservative. People want to know whether he is as conservative as his voting record."

Martin, who represented Charlotte for 12 years in Congress, said he is every bit as conservative as his record. According to a National Journal rating, he voted the conservative position 96 percent of the time on economic issues, 68 percent on foreign issues and 87 percent on cultural issues in 1982.

To win last fall, Martin said, he realized that he needed the support of Helms' New Right conservatives. "But I also realized that was not enough alone. I also had to win the support of traditional Republicans, Democrats and Independents," he added.

Democrats hold a 3-to-1 registration edge in the Tar Heel State. But euphoric Republicans, who captured three congressional seats previously held by Democrats and more local offices than at any time in state history, are talking about a party realignment here.

Martin and Helms have launched "Operation Switch" to help this along.

"We want to persuade Democrats who think like Republicans, vote like Republicans, are Republicans in their hearts -- but for various reasons register as Democrats -- to switch," Martin said in a recent interview. "We want these closet Republicans to come home to the Republican Party."

"If we could switch 100,000 voters, it would have a big impact," he added.

No one expects Martin's honeymoon to last. Although Republicans made great gains in the state last fall, Democrats still outnumber the GOP by 82 to 37 in the state House and 38 to 12 in the Senate.

Martin's best test this year will come over taxes. Like many states, North Carolina has a budget surplus, and the new governor has made cutting taxes his highest priority.

He has not disclosed details of his plan, but has outlined a proposal that offers something to rich and poor.

Martin says he wants to eliminate a 3 percent state sales tax on food and medicine -- something long advocated by labor and black groups. But he also proposes to eliminate taxes on intangible property, such as savings accounts and business inventories -- moves supported by business.

North Carolina is a low-tax state, and there is widespread opposition to the proposed cuts. But Martin said he thinks he can put together a coalition to pass the package.

"I lose some people on one part of it, but pick up people on the other," he said.