Polling on gay marriage nationally is 30% truly in favor, 55% will vote for a ban. About 7% are conflicted and split up the middle on a ban (they back civil unions) and ~8% initially appear Undecided but, with some effort by proponents, can be gotten to vote in favor of gay marriage by adopting legalistic rationales. The 55% can be split into a 40% that demands no recognition and 15% that agree to pretty minimal stuff, e.g. 'domestic partnerships'.
http://www.365gay.com/Newscon05/11/112705nhPoll.htm NH was 2% liberal relative to national average last November, Kerry won 50/49. So this polling on gay marriage or its banning, 31/58, is close to right. For a state constitutional amendment NH requires two thirds approval in both chambers of its legislature and in a popular referendum, and I think with some serious effort by activists a 40/60 split emerges should prevent passage at some or all levels.
As for the 'why', New Hampshire was initially founded as what we would now call a conservative/libertarian protest against the Puritan theocracy of Massachusetts. Not much of the state is arable land, the northern limit of where corn will grow runs about 50 miles north of the Massachusetts state line, and there isn't much in the way of minerals, so it was all about dairy farming and then some logging until fairly recently. The mountains are less eroded than Vermont's, so even dairy farming doesn't go well. It rapidly became the poorest New England state and developed a culture of rigid opposition and conservatism toward the rest, i.e. the overwhelming strength of Massachusetts. It became a regional version of Florida or Nevada for those who couldn't afford Florida during the Sixties- it still has no income tax and retirees flocked there, and they and the wacko conservatives who joined them started the 'Taxachusetts' crap there.
Lots of blue collar people who got priced out of Massachusetts and a lot of liberal-hating anti-taxation ideological Republican sorts moved out of Massachusetts to southeastern NH during the Eighties. (That's why their House district closer to Boston is more Republican than the other one.) But the southeast of the state has become exurbia for greater Boston and its New Economy as it expanded. The new people were tech economy people and insisted on better schools, which has caused a decades long fight about funding public schools, which was a brutal stalemate until the Bush economy pulled the rug out from under the blue collar locals. They realized they will become a permanent underclass if they don't educate their kids to par, i.e. kept taxes low at a price of underfunding their public schools as badly as they had all along. So prices and taxation (they have nasty nasty property taxation) have now essentially conformed to those of the Portland area in Maine and northeastern Massachusetts. The rationale to move there to evade Blue State levels of taxes and services is gone, the economy is turning Blue State, the social climate is turning Blue State, Massachusetts people now move west inside their own state rather than across the border for lower cost housing.
NH Republicans internally believe they had their last hurrah in 2002 and, like those in Colorado, they're becoming resigned to turning into a Blue State. The rumblings I hear (I'm in Mass.) are that they believe they're on their way out on the state level (could lose one or both chambers of their legislature) in '06 and can't even find a half-decent candidate to run for governor against Lynch- who seemed to be a lightweight when he first ran against Benson, but has blossomed stunningly in the year he's been in office and beaten back the state legislature's wacko Right leadership. Their (all Republican) federal Senators and House Reps suddenly stopped the wacko Right act the day after the election last year- rarely a peep out of them, a lot more moderacy in public even if they vote the DeLay line,
The wackodom isn't over yet, though. There's the abortion law business (Ayotte v Planned Parenthood of Northern New England) that they're doing in their perverse alliance with the Bible Belt reactionaries. In gay marriage matters, the next important development is probably the verdict in Cote-Whitacre v DPH next door in Mass., which should be issued later this winter.
The archetypical Old New Hampshirite attitudes are the ones you find in middle and late Robert Frost poetry. "Mending Wall" and such, though perhaps more so the ballads. He owned a farm in Derry. And you might be a little less affected by the beauty of northern New England in, say, late February and March- when everything, including the people, seems iced over and gray and cold-wet- than in July or October.