LOS ANGELES — Proponents of gay marriage, who traditionally frame the cause as a matter of equality and civil rights, are increasingly invoking something else: family. And the strategy seems to be working.

In February three state legislatures passed statutes making gay marriage legal, and in each case the appeal to family connections was a central feature.

“We need to ask ourselves: How would it feel to be a child of a gay couple?” asked Washington’s Democratic governor, Chris Gregoire, who signed the state’s legislation Feb. 13 after having announced her support for it a month earlier. “How can we tell these children that their parents’ love is seen as unequal under Washington law?”

A Washington state lawmaker who voted for the bill recalled her own marriage. “I was married for 23 years to the love of my life and he died six years ago,” said Republican Rep. Maureen Walsh in a video that went viral. “How could I deny anyone the right to have that incredible bond with another individual in life?”

In New Jersey, 15-year-old Madison Galluccio told state lawmakers debating same-sex marriage what it’s like being the adopted daughter of two gay dads.

“A lot of people think that my family is different,” she testified before an Assembly committee. “You gave us a civil union. I don’t know what that is. … It’s very hard for me to explain to my friends. It’s very hard that I can’t tell them, ‘Oh yeah, I have gay dads and they’re married just like your parents.’ But they’re not.”

Almost two weeks later, New Jersey lawmakers passed a bill legalizing same-sex marriage, but it was swiftly vetoed by Republican Gov. Chris Christie, who wants the issue decided by referendum.

In Maryland, where Democratic Gov. Martin O’Malley signed its bill into law Thursday, a Republican lawmaker had a change of heart over gay marriage after coming face to face with couples sharing their stories.

Wade Kach, left scrambling for a seat in a packed committee hearing last month, found a spot near the witness table.

“I saw with so many of the gay couples, they were so devoted to one another. I saw so much love,” said Kach, a member of the House of Delegates. “When this hearing was over, I was a changed person in regard to this issue.”

Putting a human face on same-sex marriage reflects a strategic change _ one that can pack an emotional wallop and, as Kach’s experience shows, win over the undecided or even opponents.

The message “used to be one that focused on rights, parity in benefits,” said Fred Sainz, vice president of communications and marketing for the Human Rights Campaign, a national gay rights group based in Washington, D.C.

Since about 2008, Sainz said, same-sex marriage activists have begun “talking about love, honor and commitment.”

The emphasis on family and love was prompted, in part, by two dispiriting defeats for same-sex marriage advocates at the ballot box. California voters approved Proposition 8, which banned gay marriage, in 2008. A year later, Maine voters overturned a gay marriage law there.

Framing the discussion in legal terms was not resonating with undecided voters and lawmakers, Sainz said.

The strategy is playing out in North Carolina, Minnesota and Maine, states where voters will decide the highly charged social issue in the fall.

Volunteers are sharing personal testimonials during nightly phone banks and urging undecided voters to think of any gay people they might know before they cast their votes, said Gia Vitali, spokeswoman for Minnesotans United for All Families, a group that is hoping to defeat a proposed state constitutional amendment to define marriage as between one man and one woman.

“These are our neighbors, friends and family,” Vitali said. “They are in our community, and our campaign wants to highlight the fact that we don’t want to treat them any differently.”

Meanwhile, groups opposed to gay marriage have largely followed the same script, arguing that “traditional marriage” provides children with the most ideal parenting environment. They also argue that the issue is not one of civil rights because homosexuality, they say, is a choice.

“Our messaging hasn’t changed because it’s based on truth and reality,” said Brian S. Brown, president of the National Organization for Marriage. “It’s not that complicated. You don’t need sophisticated talking points to present a common-sense truth.”

As state legislatures debated the issue in recent months, some gay marriage opponents testifying before lawmakers condemned homosexuality as a sin and warned that legalizing such unions would lead to polygamy and the promotion of homosexuality in schools.

“The scare tactics historically seem to work well for them,” said Richard Socarides, a Democratic strategist who served in President Clinton’s administration.

But Socarides and other strategists note that even some opponents of gay marriage have, over the years, softened their tone somewhat.

On its website, the National Organization for Marriage offers talking points against gay marriage, observing that “extensive and repeated polling” demonstrates that the most effective message is: “Gays and lesbians have a right to live as they choose; they don’t have the right to redefine marriage for all of us.”

And the group warns, referring to same-sex marriage as SSM: “Language to avoid at all costs: ‘Ban same-sex marriage.’ Our base loves this wording. So do supporters of SSM. They know it causes us to lose about 10 percentage points in polls. Don’t use it.”

Strategists say the debate over gay marriage has changed for several reasons, among them evolving public opinion. A Field Poll of California voters released last Wednesday, for example, found that 59 percent of respondents favored allowing gay marriage while 34 percent opposed it. Three years ago, the poll found that 52.3 percent favored allowing same-sex unions while 47.7 percent were opposed.

Such changes are fueled in part by more accepting depictions of gay and lesbian individuals in mass media. And having more people come out as gay, particularly celebrities, has liberalized public perception.

“Call it the ‘Will and Grace-ification’ of American culture,” said Dan Schnur, director of the Jesse M. Unruh Institute of Politics at the University of Southern California.

Schnur, a former Republican strategist, said those opposed to gay marriage are avoiding the strident anti-gay language common a decade ago as they try to appeal to independents.

“The harsher language is a great way of rallying your troops,” he said. But, he adds, “It makes others nervous.”