There's a risk: Republicans who decide to run with the issue in hopes of energizing their GOP base could also be seen as gay-bashers and alienate the state's political independents. There are a lot of those in New Hampshire, and they can choose either party's ballot in the Jan. 8 primary, exactly one week after the new civil unions law takes effect.
The law won't come in quietly.
"We hear reports of couples planning ceremonies for 12:01 on New Year's Eve. I'm certain this will be something that is in the news," said Fergus Cullen, chairman of the New Hampshire Republican Party. "It will remind moderates and independents in New Hampshire that they didn't plan on civil unions and same-sex marriage when they voted for Democrats last year."
Civil unions and same-sex marriage were essentially nonissues in the 2006 campaign for governor and the Legislature, then GOP-controlled. But the issue gained prominence - and unexpected success - when Democrats seized control of both houses of the Legislature that November.
Republican's campaign is already hinting at a final-week television and direct-mail campaign intended to tap opposition among core GOP voters to same-sex unions.
"Of the four leading Republican candidates, only one supports a Federal Marriage Amendment," a Romney direct mail piece told voters during the last week of November. The same piece said that "in 2004, McCain broke with Republicans and voted with Senatorsand Ted Kennedy against a same-sex marriage ban."
So far, Romney has had the most to say about the issue. Former New York Mayorsupports gay rights and stayed with a gay couple after separating from his second wife. Former Arkansas Gov. , a former Southern Baptist pastor, is amenable to civil unions. Arizona Sen. acknowledges he is uneasy when talking about the subject.
Romney often says he's against discrimination but cannot embrace same-sex civil unions. He says, "Marriage is an institution which is designed to bring a man and woman together to raise a child."
Could it be an effective wedge issue, exploiting voters' own discomfort about the issue?
"I don't think it will work, not in New Hampshire," said Charlie Black, a McCain adviser and a veteran of the past three Republican presidential campaigns. He is advising McCain not to make civil unions a key part of his campaign's final weeks.
A big question is which primary the independents will vote in, Republican or Democratic.
Registered independents - or undeclareds, as they are called in New Hampshire - outnumber both Republicans and Democrats in the first-primary state. Though polls have indicated that most plan to vote in the Democratic primary, a blowout on either side in the Jan. 3 Iowa caucuses could prompt many of them to vote in the New Hampshire primary in which they think they can make a difference.
There has been no public polling to suggest civil unions would be a huge mover, but the increased visibility of the issue could be a boon for Romney as he tries to solidify the last bits of support among his party's base. He trails Huckabee in Iowa and is in a tight race with him in New Hampshire, according to the latest AP-Ipsos polling.
University of New Hampshire pollster Andrew Smith said more Republicans than Democrats opposed civil unions in a survey last spring. Most of the opposition came from older voters - who traditionally vote and are on direct-mail and activist lists.
Republican campaign advisers, speaking on condition of anonymity when discussing internal strategy, know that New Hampshire independents might be turned off if the campaigns go too far. But they said not raising the issue might brand a candidate as weak among party activists.
"There are lots of people who are tolerant of other lifestyles who nonetheless don't believe in same-sex marriage and think that Democrats in New Hampshire made a mistake when they allowed that this year," said Cullen, the state GOP chairman.
On the other hand, when Democratic Gov. John Lynch signed the law in May, some conservatives predicted he would take a hit in the polls. It didn't happen, and in July the second-term governor still had 76 percent support, according to a University of New Hampshire poll for CNN and WMUR-TV.