Hartford, Conn. ? Now that the Connecticut Supreme Court has ruled same-sex couples have the right to wed, opponents of gay marriage are pinning their hopes on an infrequent ballot question in a longshot bid to block the unions.

Every 20 years, voters can force a convention during which delegates can rewrite the entire constitution. It’s a long, painstaking process that could cost millions and, by coincidence, it’s on the ballot this November.

“This is our one opportunity for the people to have a voice, for the people to be heard, for them to decide whether marriage will be protected as between a man and a woman,” said Peter Wolfgang, executive director of the Family Institute of Connecticut.

On Friday, the state Supreme Court ruled that Connecticut would be the third state, after California and Massachusetts, to allow gay marriage. The court said Connecticut’s 2005 civil union law doesn’t give same-sex couples the same status as married heterosexual couples.

Unlike California, where next month’s ballot referendum will decide whether to outlaw gay marriage, Connecticut voters are being asked to consider only if they want a constitutional convention. If so, convention delegates would be appointed by the state General Assembly, which is largely comprised of Democrats who are sympathetic to same-sex issues.

State Rep. Mike Lawlor, co-chairman of the legislature’s Judiciary Committee, said he’s not sure everyone understands the constitutional convention process.

“It is a very elaborate, months-long process in which a group of people basically rewrite the whole state constitution,” he said. “It costs millions of dollars and requires a special statewide election. If you just want to make a specific amendment to it, which it sounds like they are talking about, then there is a lot easier way to do it.”

That would be the legislative amendment process, which typically requires a three-quarters vote of both General Assembly houses to put a constitutional amendment on the ballot.

Wolfgang said his group has not ruled out seeking an amendment from lawmakers, but is focusing on getting out the “yes” votes in November.

“The real battle will be Election Day,” he said. “Even in a state with a legislature as liberal as ours, we have defeated our opponents year after year through the legislative process. They could never have gotten same-sex marriage through the Democratic process. Democracy is gay marriage’s worst enemy.”