Sutton and two other judges from the 6th Circuit heard arguments in six cases from Ohio, Kentucky, Michigan and Tennessee in the biggest such session on the issue so far. The cases pit states' rights and traditional, conservative values against what plaintiffs' attorneys say is a fundamental right to marry under the U.S. Constitution.
If the 6th Circuit decides against gay marriage, that would create a divide among federal appeals courts and put pressure on the U.S. Supreme Court to settle the issue for good in its 2015 session. The appeals panel did not indicate when it would rule.
Another judge on the panel criticized Sutton's argument Wednesday, saying that sometimes courts need to intervene when constitutional rights are being violated.
Judge Martha Craig Daughtrey, a Clinton nominee, pointed out that it took decades for women to win the right to vote.
"Do you have any knowledge of how many years I'm talking about, going into every state, every city, every state board of elections, for 70 years?" Daughtrey said of women's efforts to get the vote. "It didn't work. It took an amendment to the Constitution."
In their lines of questioning, both Daughtrey and Deborah L. Cook, a George W. Bush nominee, all but showed how they would rule, but Sutton vigorously questioned attorneys on both sides of each case.
Sutton, also a Bush nominee, is known for being unpredictable, shocking Republicans in 2011 when he became the deciding vote in a 6th Circuit ruling that upheld President Barack Obama's health care law.
The afternoon of arguments opened with Michigan's solicitor general, Aaron Lindstrom, saying that any change in the state's ban on same-sex marriage should come through the political process.
"The most basic right we have as a people is to decide public policy questions on our own," he said.
Fundamental constitutional rights shouldn't be decided in popular votes, countered attorney Carole Stanyar, who represents the plaintiffs in that case.
"The Michigan marriage amendment gutted the democratic process," she said.
In Ohio's cases, Cincinnati civil rights attorney Al Gerhardstein of Cincinnati said the state's refusal to recognize out-of-state gay marriages violates the dignity of same-sex couples and amounts to unique discrimination, since Ohio has historically recognized marriages in other states that wouldn't be legal in Ohio, such as between cousins or involving minors.
Eric Murphy, Ohio's state solicitor, said Ohio has traditionally defined marriage as between a man and a woman and that same-sex marriage is too new to be considered a deeply rooted, fundamental right.
Outside the courthouse in nearby Fountain Square, advocates held up banners and signs urging freedom to marry. Jon Bradford, 26, of Covington, Kentucky, wore a wedding dress, and his partner, Matt Morris, wore a top hat and formal shirt.
"It's to make a statement, really," Bradford said. "We want to be married."