If gay marriage was legal more gay people would become Republicans. Not overnight but given time with gay issues off the political agenda more gay people would become Republicans. Gay men tend to be wealthier than straight people on average. Also groups like Pink Pistols promote 2nd amendment rights so gays can defend themselves against homophobes. And then there's foreign policy. Since the Islamic world is virulently homophobic gay people will be more inclined to support an aggressive foreign policy at least when enough time has passed and the association effect from Democrats supporting gay rights and a less aggressive foreign policy has subsided.
This may underly why Democrats dragged their feet on gay rights but always made sure they were more in favor than the Republicans.
Homosexuals do not seek the right to marry, as they already have this right just like everyone else; they seek special rights which are unfounded. This country was founded on judeo-christian principals and homosexual activity is not consistent with the definition of marriage. Marriage is a union between one man and one woman and is designed in a way which compliments the joining of two bodies into one unit. As homosexuals are incapable of this union; allowing them to call their relationship marriage will only serve to further deteriorate the moral fabric under which this country was formed.
I am a supporter of gay marriage. Though I do not believe it will benefit republicans. But neither will it dis-benefit them. Really I don't see how gay marriage Positively/Negatively influences anyone other than gay people themselves. The only way I see it positively influencing anyone other than gays is that supporters would be happy if it was legalized. And it would only negatively influence those who are against it by making them upset that it didn't get through. And vice versa depending on the state.