Deep in the Bible Belt, new signs emerged this weekend of evolving views among Republican governors on gay marriage.

While the Republican Party's religious conservatives continue to fight against same-sex marriage, its governors appear to be backing off their opposition – in their rhetoric, at least. For some, the shift may be more a matter of tone than substance as the GOP tries to attract new voters ahead of the midterm elections. Nonetheless, it is a dramatic turn for a party that has long been defined by social conservative values.

"I don't think the Republican Party is fighting it," Wisconsin's Republican governor, Scott Walker, said in an interview this weekend at the National Governors Association in Nashville.

"I'm not saying it's not important," continued Walker, who is considering a 2016 presidential bid should he survive his reelection test this fall. "But Republicans haven't been talking about this. We've been talking about economic and fiscal issues. It's those on the left that are pushing it."

Walker, like other ambitious Republican governors, is trying to strike a delicate balance. His comments come just days after he formally appealed a federal judge's ruling striking down Wisconsin's ban on same-sex marriages, a ban he supported. But after his party's disastrous 2012 election, the Republican National Committee commissioned a report calling for more "inclusive and welcoming" tones on divisive social issues – particularly those "involving the treatment and the rights of gays”.

Walker explained his court appeal as simply as his obligation as governor to defend the state's constitution.

Other Republican governors, however, including New Jersey's Chris Christie, opted against appealing similar rulings, clearing the way for gay marriage to become legal.

"That is a very controversial and divisive issue," said Iowa governor Terry Branstad, suggesting Republicans are better served by focusing on economic issues. "I'm a religious conservative, I'm a Catholic, I'm pro-life. [But] I think the people of Iowa look to me to provide leadership in bringing good jobs and growing the Iowa economy."

A Gallup poll found in May that national support for same-sex marriage reached an all-time high of 55%. That includes 30% of Republicans and nearly eight in 10 young adults from both parties.

Courts across the nation repeatedly have struck down gay marriage bans. The latest such ruling came on Wednesday in Colorado, but it's on hold pending an appeal. At least 20 states now allow gay marriage, although the issue may be headed for the supreme court.

The high court's landmark ruling last summer allowed married same-sex couples to receive the same federal benefits as other married people but did not specifically address whether gay marriage is a constitutional right.

Democratic governors in Republican-leaning states that have banned gay marriage also appear to have softened their stands. Many said they were looking to the supreme court to resolve the issue once and for all.

Like Walker, Kentucky's Democratic governor, Steve Beshear, is appealing a recent court ruling that struck down his state's gay marriage ban.

"My goal is to get that issue to the United States supreme court and get a final decision that will tell us all what the law is going to be in the future, and then Kentucky will abide by it," Beshear said.

Walker, too, said that Republican governors would be "legally obligated" to support gay marriage should the supreme court rule in its favor.

For now, the Republican Party's official platform, as adopted in 2012, calls for a federal constitutional amendment defining marriage as "the union of one man and one woman”, while formally supporting Republican-led campaigns to make the same change in state constitutions.

And despite the softening rhetoric, several states are continuing to fight. Tennessee, Ohio, Michigan and Kentucky are scheduled to present arguments against recent gay marriage rulings in their states before the 6th US circuit court of appeals in Cincinnati on 6 August.