Lawyers for the 26 states challenging the constitutionality of the nation’s new health-care law squared off against the Obama administration in an appeals court in Atlanta on Wednesday, where a panel of three judges asked tough questions of both sides.

One judge, Frank M. Hull, appeared more sympathetic to the law — at one point interrupting an attorney for the states to tell him that his central argument “doesn’t get me very far.”

Nonetheless, the case before the U.S. Court of Appeals for the 11th Circuit could offer the armada of Republican state leaders who have taken on the law their best chance of a win during stage two of a multi-pronged, protracted legal battle widely expected to end in the Supreme Court.

More than 30 suits have been filed since the Affordable Care Act was adopted in March 2010, nearly all by individuals and organizations. Appellate courts in Richmond and Cincinnati have heard arguments in three of the cases over the past several weeks, including one filed separately by the state of Virginia.

The three judges who heard that case last month, along with another lawsuit brought by private parties in Virginia, were appointed by Democratic presidents, including two named by President Obama. And they spent considerable time questioning whether Virginia even has standing to sue.

By contrast, the three judges randomly assigned to the multi-state suit in the Atlanta court Wednesday are a more diverse group: Although both Hull and Judge Stanley Marcus were appointed to their current posts by President Bill Clinton, Marcus was first tapped for the federal bench by President Ronald Reagan.

Chief Judge Joel F. Dubina was named by President George W. Bush.While a judge’s political connections do not indicate how he or she will rule, so far lower courts have cleaved along markedly partisan lines: Four federal district judges appointed by Democratic presidents have upheld the law’s constitutionality. Two named by Republicans deemed it invalid.

At issue in all these cases is whether Congress overstepped its constitutional authority to regulate commerce when it included a provision in the Affordable Care Act that requires virtually all Americans to obtain health insurance after 2014 or pay a fine.

The district judge who heard the Virginia case struck down the insurance mandate but found that the rest of the law could remain intact. In the multi-state lawsuit on appeal in Atlanta, the lower court judge, Senior U.S. District Judge Roger Vinson, invalidated the entire law, reasoning that the insurance requirement was inextricably linked with the rest of the statute.

Vinson, did not, however agree with the states’ claim that the legislation violated the Constitution by requiring states to cover a larger share of the poor through Medicaid, which is funded by federal and state money.

During the nearly three-hour appellate hearing Wednesday, the judges appeared open to reconsidering that question, if not necessarily convinced of the legal arguments.

However, they spent most of their time grappling with how to characterize a person’s decision not to buy health insurance.

Paul D. Clement, a solicitor general under President George W. Bush who is representing the states, argued that it is a form of inactivity akin to people “sitting in their living room.” So legal precedents establishing Congress’s right to regulate economic “activity” under the Constitution’s commerce clause do not apply.

Judge Stanley Marcus seemed to agree when he pressed the administration’s lawyer, Acting Solicitor General Neal K. Katyal, to come up with an example in which the Supreme Court used the commerce clause to justify “compelling a private person to purchase a private product.”

Judge Joel F. Dubina similarly observed that “I’ve read all the Supreme Court cases. I can’t find one like this.”

Katyal repeatedly countered that the question was irrelevant because a person’s choice not to buy insurance is not inactivity but rather an economic decision about how to pay for the health care they will inevitably need.

Those who obtain insurance are effectively paying for that care now, through premiums, he said. Those who forgo it are opting to pay later, either out of pocket or by passing the cost on to hospitals, which cannot turn away the uninsured and must therefore pass the burden on to governments, insurers and, ultimately, paying customers.

Hull appeared to agree, impatiently waving off Clement each time he tried to make his inactivity argument.

“This activity-inactivity thing doesn’t help me, personally,” she said. But she joined the other judges in pressing Katyal to explain why upholding the insurance mandate would not open the floodgates for Congress to compel the purchase of any number of products ranging from fire insurance to energy efficient cars for society’s betterment.

Katyal said the health-care market has several unique characteristics: Nearly everyone will have to consume health-care at some point. If they cannot afford life-saving care hospitals and providers are nonetheless legally required to treat them. And when that happens the cost will be shifted not merely onto the government but to other private individuals.

“Health care is different in this specific way,” he said. “That’s what stops the slippery slope.”

The states party to the lawsuit are Alabama, Alaska, Arizona, Colorado, Florida, Georgia, Idaho, Indiana, Iowa, Kansas, Louisiana, Maine, Michigan, Mississippi, Nebraska, Nevada, North Dakota, Ohio, Pennsylvania, South Carolina, South Dakota, Texas, Utah, Washington, Wisconsin, and Wyoming. Two individuals have also joined the suit.