Based on party lines, House and Senate Republicans both have veto-proof majorities. But this is an issue where party allegiance gets muddy.

In a state whose “Live Free or Die” motto figures into many a policy decision, even many opponents of same-sex marriage wish the issue would just disappear. Republican lawmakers with libertarian leanings, a sizable group, seem especially unhappy to be facing a repeal vote, as well as those who maintain that cutting spending should be the legislature’s sole concern. Both groups appear worried about a backlash from their constituents.

Representative Andrew Manuse, a Republican, said in an e-mail that he would support a repeal because he objected to government “using its power to redefine a religious, social and societal institution.” But he added, “I really am not focusing on this issue.”

Should the repeal pass, New Hampshire would be the first state in which a legislature has reversed itself on the issue of same-sex marriage.