Gay-marriage advocates such as Sainz contend that the issue works to their advantage because of greater intensity on their side. In the Virginia race between Herring and Republican Mark D. Obenshain, one Fairfax County voter who fought successfully to have his provisional ballot accepted told Herring he followed through because of his views on same-sex marriage.

“I am gay, and I got an e-mail from the Human Rights Campaign urging me to vote for you,” the voter told Herring in a phone message, according to the attorney general’s aides. “I want you to win to protect not only my rights, but everyone’s rights.”

Herring ended up winning by 907 votes out of 2.2 million cast.

Same-sex marriage can bring progressive voters to the polls. When Minnesota rejected a constitutional amendment to ban gay marriage 2012, the proposal received more votes, pro and con, than were cast in the presidential contest.