If the issue of same-sex marriage is on an expressway to the Supreme Court, Wednesday was rush hour in a federal appeals court here.

In an unprecedented and marathon hearing, tag teams of attorneys for four states told an appellate panel why voter-approved prohibitions in Kentucky, Michigan, Ohio and Tennessee should be honored.

All the while, plaintiffs and their families filled row after row of a huge, ornate courtroom, arms around one another, occasionally shushing babies and listening for their names to be mentioned.

It became clear after three hours of arguments that the panel could become the first roadblock for proponents of same-sex marriage who have had an extraordinary winning streak in knocking down state restrictions following a landmark decision by the Supreme Court in 2013.

That 5 to 4 ruling struck down the part of the federal Defense of Marriage Act that defined marriage as only between a man and a woman.

But a panel of three randomly chosen judges of the U.S. Court of Appeals for the 6th Circuit left questions about whether it would follow the lead of two other appeals courts. Those courts said the reasoning of the Supreme Court’s decision meant that states lacked the right to limit marriage to opposite-sex couples and to deny recognition of unions conducted elsewhere.

Appeals Court Judge Jeffrey S. Sutton repeatedly asked attorneys representing the same-sex couples why they didn’t think it better to win marriage rights systematically through the democratic process, capturing the “hearts and minds” of their fellow citizens instead of “five votes of the Supreme Court.”

Because overturning state constitutional amendments is difficult, time-consuming and expensive, they answered. And Alphonse A. Gerhardstein, representing same-sex couples married elsewhere who want Ohio to recognize their unions, said it is wrong to make a fundamental right dependent upon popular approval.

Such rights should not be subject to popular vote, Gerhardstein said.

His clients, he said, have children who can have only one of their parents officially recognized. “They deserve two parents,” he said. “They deserve them now.”

A more conservative panel

A loss might not be the worst thing for proponents of same-sex marriage, who are eager to get the issue to the high court. Even in those states where courts have struck down bans, Supreme Court justices have blocked marriages until the appeals courts or the high court itself decides the issue.

Although the justices in 2013 ruled 5 to 4 in U.S. v. Windsor that the federal government could not refuse to recognize same-sex marriages performed in those states where it is legal, the court did not decide whether states, the traditional guardian of marriage laws, may ban such unions.

Although two appeals courts have ruled that bans in Oklahoma, Utah and Virginia violate the federal Constitution, the Supreme Court is under no obligation to review those decisions.

But if there is a split among the appeals courts on whether marriage is a fundamental right that must be offered to all or, alternatively, that states are free to restrict it to heterosexual couples, that would almost surely require Supreme Court intervention sooner rather than later.

The 6th Circuit is more conservative than the two appeals courts that have ruled. It has twice as many judges nominated by Republican presidents as Democratic ones, and the panel of judges hearing the cases precisely reflects that split.

Sutton and Circuit Judge Deborah L. Cook were nominated by President George W. Bush, and Senior Circuit Judge Martha Craig Daughtrey was chosen by President Bill Clinton.

Daughtrey left little doubt where she came down on the issue. She repeatedly invoked civil rights struggles of the past, and compared the cases to Loving v. Virginia, a 1967 decision that said bans on interracial marriage were unconstitutional.

She repeatedly drew laughter from the crowd with tough questions for the states’ lawyers and sometimes caustic asides. When Ohio Solicitor General Eric Murphy said voters in the states are free at any time to change their minds and allow same-sex marriage, she asked him if he knew how long it took women to win the right to vote.

“Seventy-eight years,” she said, of trying to persuade states and localities to grant the franchise before an amendment to the Constitution finally settled the issue.

She said she wasn’t asking Murphy to respond. “I just thought you’d like to know that if you’re ever on ‘Jeopardy,’ ” she said.

Cook made few comments during the proceedings, but she seemed inclined to side with the states. The couples in Ohio were aware that the state would not recognize their marriages when they moved there, she said. And she worried about the courts undermining voters, who approved the bans overwhelmingly.

A judge is scrutinized

That left Sutton as the most closely watched. A former clerk to Justice Antonin Scalia, he made a name for himself as a lawyer before the Supreme Court as a vigorous advocate for federalism. Liberal groups fought his nomination for two years, partly because he was considered a potential Supreme Court choice in a Republican White House. His clerks often move on to similar positions at the high court, usually in the chambers of the court’s conservative members.

“He is seen as an influential judge outside the circuit,” said Pierre Bergeron, a Cincinnati lawyer who maintains the 6th Circuit Appellate Blog.

Supporters of same-sex marriage are concerned about an article that Sutton wrote this year for the Harvard Law Review. “Count me as a skeptic when it comes to the idea that this day and age suffers from a shortage of constitutional rights,” he wrote.

But in one significant case, Sutton was a surprise and a disappointment to conservatives: He held that Congress had the power to pass the Affordable Care Act.

On Wednesday, Sutton gave both sides reason for hope and concern. The question came down to whether states had the right to define marriage, he said.

He debated the lesson of Loving, saying that if a white man and a black man had applied for a marriage license the next year, it was clear that they would have been denied. And he said Windsor addressed the federal government’s attempt to intervene in an area — marriage — that had traditionally been left to the states.

Don’t states deserve the benefit of the doubt in trying to preserve the definition of marriage that has prevailed for ages, he asked.

On the other hand, Sutton seemed to side with Daughtrey in questioning the state’s proffered reason for restricting marriage to heterosexual couples: encouraging procreation and increasing the chances that a child would be raised in a home with a mother and a father.

He also said that although the message of the Supreme Court’s Windsor decision may be ambiguous, the “trajectory” is clear: more recognition and protection of gay rights.

The panel has no deadline for deciding the cases. By the time it does, it is likely that at least three other appeals courts will have heard challenges.