Conservative supporters of the bans have turned their eyes toward Justice Ruth Bader Ginsburg. The justice, a Clinton appointee, told a Columbia University forum in 2012 that the 1973 Roe v. Wade decision that struck down state bans on abortion short-circuited a political consensus on abortion rights.
Karl Rove, the onetime strategist for former President George W. Bush, told ABC's "This Week" on Sunday that Ginsburg may oppose a sweeping decision in support of same-sex marriage.
"What we may see is a decision here that in essence is not a 5-4 decision, but a 6-3, 7-2 that says 'leave it up to the states,' " said Rove, whose old boss once endorsed an amendment to the U.S. Constitution to ban same-sex marriages. "In fact, we could see an 8-1."
CNN legal analyst Jeffrey Toobin, the author of a lengthy Ginsburg profile for The New Yorker, said Ginsburg is likely to find the Defense of Marriage Act unconstitutional but isn't likely to knock down bans on same-sex marriage nationwide.
"She does not believe in grand pronouncements, even liberal grand pronouncements, from the Supreme Court," Toobin said.
A shifting landscape
The court is hearing arguments as a public shift toward same-sex marriage appears to be gathering speed. The proportion of Americans who support same-sex marriage has grown from around 40 percent in 2007 to 53 percent in a CNN/ORC International poll conducted last week; 44 percent remain opposed.
Barack Obama ran for president in 2008 as a supporter of civil unions but not same-sex marriage. In 2012, months before facing voters again, he said his thinking had shifted and that he supported marriage rights for gays and lesbians.
"I had hesitated on gay marriage, in part, because I thought civil unions would be sufficient," he said. "I was sensitive to the fact that -- for a lot of people -- that the word marriage is something that provokes very powerful traditions and religious beliefs."
Obama's Republican challenger, Mitt Romney, ran as a defender of traditional marriage, and the party's platform opposed same-sex marriages. But since November, numerous GOP figures have emerged as supporters of same-sex unions.
Dozens of high-profile Republicans -- including former party Chairman Ken Mehlman, ex-presidential hopeful Jon Huntsman and actor Clint Eastwood -- filed a friend-of-the-court brief arguing that Proposition 8 should be struck down. And earlier this month, Sen. Rob Portman of Ohio announced he is now a supporter of the freedom to marry after finding out that his son -- a Yale sophomore -- is gay.
"Eventually, as time marches on, this is a country that believes pretty squarely in marriage equality," former Bush spokeswoman Nicolle Wallace told "Fox News Sunday."