James Esseks, national director of the LGBT Project at the A.C.L.U., agreed. “No question this issue will get back to U.S. Supreme Court over the next several years,” he said.

At the heart of many of the cases is the issue the Supreme Court ducked in one of its two recent rulings, a narrow decision on a California case: If a state prohibits same-sex couples from marrying, does it trample the guarantee of equal protection in the United States Constitution?

Supporters believe that enlarging the map of states that allow same-sex marriage will ultimately influence the Supreme Court when it next takes up the issue of a constitutional right to same-sex marriage, as it is expected to do in the next few years. Activists are pressing legislatures in three more states that appear ready to pass measures legalizing same-sex marriage: New Jersey, Hawaii and Illinois.

“We think what the map of the country looks like is going to make a big difference to how the issues in the case feel to the Supreme Court,” Mr. Esseks said. “Will we have the 13 states plus D.C., or will we be at 20 or more?”

Opponents are fighting back under the same logic. They see an opportunity to add Indiana to the 29 states with constitutional bans on same-sex marriage.

“Our challenge is to let the court see they’re not going to get away with this without a massive public revolt,” Mr. Schubert said.