PROVIDENCE, R.I. – When Laura Pisaturo knocks on doors, she talks about the economy and jobs. The Rhode Island Senate candidate is gay and wants the state to join most of New England in recognizing same-sex marriage. But she doesn’t talk about it that much on the campaign trail.

“Top on everyone’s minds is jobs and the economy,” said Pisaturo, a former state prosecutor seeking to unseat longtime Sen. Michael McCaffrey, D-Warwick, in Tuesday’s Democratic primary. McCaffrey opposes gay marriage.

While jobs and Rhode Island’s battered economy continue to loom large in the minds of voters and candidates alike, a quiet battle over gay marriage in this year’s legislative races could significantly alter the makeup of the General Assembly while potentially determining whether Rhode Island joins Connecticut, Massachusetts and four other states in recognizing gay marriage.

An energized and well-organized coalition of supporters are backing candidates that they hope will tilt the legislature in favor of same-sex marriage. But Ray Sullivan, campaign director for the gay-marriage advocacy group Fight Back Rhode Island, said candidates must talk about more than marriage if they hope to win. The state’s 10.8 percent unemployment rate remains the second-highest in the nation, and taxes, education and economic development remain pressing priorities.

“I don’t think any of the candidates we’re working with are single-issue candidates,” said Ray Sullivan, campaign director for Fight Back Rhode Island, a group that’s pushing for gay marriage. “They’re pro-equality, but they’re also pro-jobs.”

Same-sex marriage is legal in New York, Connecticut, Iowa, Massachusetts, New Hampshire, Vermont and Washington, D.C. Maine, Maryland and Washington will vote this fall on proposals to authorize gay marriage. Minnesota voters will be asked whether they want to prohibit gay marriage in their state constitution.

The marriage question is almost certain to come up in Rhode Island when state lawmakers convene in January. House Speaker Gordon Fox has vowed that if he retains his post, he will call for a House vote on gay marriage early in the new year. Fox, who is openly gay, dropped gay-marriage legislation last year after it became apparent it wouldn’t pass the Senate, where President Teresa Paiva Weed is a notable opponent. This year, he said, he’ll “work his backside off” to advance the issue.

“We are in a New England state and you can easily go across the state line to get married,” Fox said. “I want to have my marriage in the state of Rhode Island.”

Advocates are betting that if enough supporters of gay marriage are elected to the Senate Paiva Weed will agree to hold a vote. “It would be the responsible thing to do for Senate leadership to move forward with this issue,” Sullivan said.

Paiva Weed did not respond to multiple requests for an interview. Her spokesman, Greg Pare, said Paiva Weed believes it is “premature” to speculate as to what the Senate will do with same-sex marriage.

Last year the General Assembly approved civil unions for same-sex couples that guarantee the same state rights and benefits as marriage. The response has been lukewarm: Just 68 couples have sought civil union licenses in the first year since they were first available.

McCaffrey, who’s facing a tough challenge from Pisaturo in a district he’s represented since 1994, said he supported civil unions but remains opposed to gay marriage. But he said he’s more focused in telling voters about what lawmakers have done to rein in pension costs, increase education funding and streamline business regulations.