Can America's only no-tax state survive the 'new federalism'?

In New Hampshire, it's called ''the pledge.'' And no candidate for governor has been elected without taking it.

But times are changing and this year's candidates may be less willing to make the traditional promise to shun a state income or sales tax.

Nobody in New Hampshire, least of all those holding state office, would welcome the change. But prospects for holding the line against these two stalwarts of state revenue raising appear to be fading.

The state is expected to make it through the year without a major new revenue boost. Yet many close to the scene, including some legislators, are less optimistic about 1983. The tax issue becomes even more important as President Reagan talks about returning many federal programs - and their funding - to the states.

New Hampshire is now the only state with neither a sales tax nor a broad-based income tax. Alaska, Delaware, Montana, and Oregon have no sales tax. Connecticut, Florida, Nevada, South Dakota, Tennessee, Texas, Washington, and Wyoming have no personal income tax. But only the Granite State has neither one. (Although wages and other forms of earned income are untaxed in New Hampshire, interest and dividends on investments are taxed.)

Particularly on the spot in New Hampshire could be Gov. Hugh J. Gallen. His third-term candidacy, now all but certain, would hardly be boosted were he to hint new or higher taxes are in the offing.

Yet at this point he is shying away from commitment, beyond this year, to veto any measure that might involve a major new tax, such as one on payrolls that was supported by a majority of state representatives in a straw vote last spring.

Governor Gallen frankly concedes that eventually there may be little choice but to tap one of these revenue sources. Much could depend, he asserts, on the extent of federal funding cutbacks. Budget-squeezing efforts will continue in the Granite State, he emphasizes, adding that if and when a major new tax is considered, it must be accompanied by overall tax restructuring.

''There is no question many of our existing taxes are unfair and there is little question we must begin to seriously consider far-reaching reform of the tax system,'' he says, noting that ''many people - all with the highest intentions - believe that new taxes are the answer'' to the mounting fiscal challenge.

This comes at a time when Gallen and other state officials from both political parties are under increasing pressure from the cities and towns for increased aid for schools to head off climbing property taxes.

While state taxes overall are the lowest in the nation, thanks largely to the avoidance of levies on earned personal income and sales, the local property taxes throughout New Hampshire are among the highest and fastest growing across America.

The governor makes it clear that under no circumstances would he favor expanding the state's revenues through the legalizing of casino gambling. Such activities, he maintains, would have a negative impact on New New Hampshire life style.

Whether the Granite State resorts to a new broad-based tax could hinge on the recommendations of a special panel formed by the governor to explore funding alternatives.

Some observers outside the Gallen administration suggest that if the panel concludes that a substantial new tax is all but unavoidable, it is unlikely Gallen would again ''make the pledge'' as he did in the 1978 and 1980 campaigns, and as has Republican Meldrim Thomson Jr., his three-term predecessor, since at least 1970. Whether Mr. Thomson will make a third try to regain the governorship is keeping everyone guessing.

Although no contender has formally declared, regardless of what former Governor Thomson does, State Senate president Robert Monier of Goffstown is considered a sure GOP contender. Other possible GOP contenders are Louis D'Allesandro of Manchester and college Prof. John H. Sununucq of Salem.

Emergence of a formidable challenger to Governor Gallen for the Democratic nomination is generally viewed as unlikely.