As he has done so many times before, New Hampshire Gov. Meldrim Thomson Jr. has plunged headlong into a controversy so divisive that it could mortally wound the political careers of most governors.

But as he has also done so often, Thomson, now in his third term, seems to be on the verge of extricating himself from the mess relatively unscathed - and possibly with increased support.

The controversy this time centers around his handling of more than 2,000 anti-nuclear-power demonstrators who on May 1 staged a sit-in at the construction site of a $2 billion nuclear plant at Seabrook, a tiny community near the coast in the southeastern corner of the state.

It was the first massive show of civil disobedience against a nuclear power plant in the United States, and it is viewed by the sponsoring Clamshell Alliance as a precursor to a national movement comparable in spirit to the Vietnam era protests.

Thomson, after weeks of escalating rhetoric, in which he charged the demonstrators with having "terrorist" connections, ordered their arrest once they refused to leave a tent city they had been allowed to set up on a parking lot at the nuclear site. Police rounded up 1,414 of them over a 14-hour period.

Supporters of the Clamshell, a coalition of ecology groups and militant organizations carried over from the anti-war years, accused Thomson of reneging on a promise that they could stay on the site indefinitely. Then, when the state ordered them held in bail in makeshift jails at five national guard armories jails at five national guard armories on trespass charges, the protesters accused Thomson of being vindictive. During the major disturbances of the '60s, demonstrators were released on their own recognizance in order to facilitate processing.

About 700 of the New Hampshire demonstrators are still being held.

But the real outcry came from Thomson's fiscally conservative supporters within Thomson's administration that the governor's decision to prosecute and incarcerate the protesters would cost the state $1 million at a time when it faces a $51 million deficit over the next two years.

Thus, for many New Hampshire residents, who polls show heavily favor nuclear energy, these aspects of the Seabrook clash have smothered the issue of the safety and practicality of reactors.

In effect, Thomson's handling of a new to Thomson, who once proposed arming the National Guard with tactical nuclear weapons, who aroused the anger of Jews by lowering the state house flag to half mast on Good Friday, and who attracted the ire of liberals when he did the smae the day after President Carter declared amnesty to draft resisters.

A national chairman of the Conservative Caucus, Thomson, has long been allied with William Loeb, the combatively conservative publisher of The Manchester Union Leader.

In his first months in office, Thomson was accused of examining the tax records and police files of his political enemies.

He has since aroused emotional opposition from the 400-member state legislature by vetoing a capital budget it had spent months preparing.

His own cabinet officers were made unhappy by his firing of officials who disagreed with him and opposed his policies in public.

And he fued with environmental coalitions goes back to his support of a 1974 Aristotle Onassi proposal to build an oil refinery on New Hampshire's narrow stretch of ocean frontage.

Yet through all of the turmoil and political rancor, Thomson has demonstrated an almost uncanny ability to survive intact.

"He's like a cat. He's got nine lives. He'll jump off a roof and always landon his ffet," said Democratic state Sen. Delbert F. Downing, the senate minority leader.

Malcolm McLane, former mayor of Concord and now a Republican member of the governor's Executive Council, siad, "Considering the ever-increasing numbers of people who vote for him, I don't think his political career is over yet. I'd like to say it's the end of him, but this thing will taper off." McLane is one of many Republican officials who frequently fued with the governor over what they feel are precipitous actions.

"One thing he likes to do is do things unilaterally. This was made for him - a police action - but it will be very difficult for him to go to the legislature and ask for a 10 per cent cut in state jobs when he has spent $1 million on his Seabrook folly," said C. Robertson Trowbridge, Senate Finance Committee chiarman and owner of the Yankee Publishing Co., which publishes the Farmers Almanac.

Thomson, however, seems to have partly muted the cost issue by revising downward the expenses estimate and by announcing that the state is applying to the U.S. Law Enforcement Assistance Administrationf or a $669,000 grant to defray expenses.

Also, he issued an appeal for contributions from corporations, unions and individuals across the union, saying, "Our battle today can become theirs tomorrow."

In New Hampshire, taxes is the most dominant issue. It is as volatile a question here as was race in the South.

Thomson has twice won re-election by refusing to consider an income tax or sales tax. As a result, the verage direct taxes are $210, the lowest in the nation, with most revenue coming from levies on liquor sales, business profits and other indirect taxes.

Thomson's image of frugality has overwhelmed his challengers, making him particularly popular with the fiscally conservative Franco-American population and people who moved here to escape the big government-and-tax spiral that has engulfed neighboring Massachusetts.

State Democratic Chairman Joanne-Symons, while calling Thompson "an irresponsible demogogue," begrudgingly admitted his success on the tax issue.