Hashim Mooppan, a lawyer with the U.S. Justice Department, represented Kennedy and other parties that are defending the ACA preventive services package construction process.

Even though the case could affect whether the ACA continues to require employers to cover services such as checkups for workers and cancer screenings for workers, the oral arguments had nothing to do with the health benefits.

Related: Employers' ACA coverage in limbo as Supreme Court weighs task force legality

Instead, the lawyers and the justices focused on whether Congress created rules that are compatible with the U.S. Constitution's appointments clause when it had HHS use an advisory board, the U.S. Preventive Services Task Force, to choose part of the ACA preventive services package.

The backdrop: President Barack Obama signed the two bills that created the ACA package in 2010.

The ACA requires employer-sponsored major medical plans created or changed significantly since 2010 to cover the services in the ACA preventive services package without making covered patients first pay deductibles, co-payments or other out-of-pocket costs.

The U.S. Constitution appointments clause requires that officers of the president be appointed by the president and confirmed by the Senate.

Past Supreme Court rulings have distinguished between "principal officers," who must be appointed by the president and confirmed by the Senate, and "inferior officers," who can be chosen by presidential officers and serve without getting confirmed by the Senate.

The U.S. Preventive Services Task Force, an advisory board that existed before 2010, is supposed to provide recommendations for any items that go into the package other than recommendations for vaccines, pediatric services and women's health services.

The Braidwood case: Braidwood and its supporters say the construction of the U.S. Preventive Services Task Force is unconstitutional because Congress gave the HHS secretary or an official under the secretary the authority to choose the task force members, emphasized that the task force members should be independent and have independent authority over the preventive services package components, and failed to have the task force members appointed by the president or confirmed by the Senate.

In 2022, a federal judge in Texas ruled in favor of the plaintiffs. Last year, the 5th U.S. Circuit Court of Appeals agreed with the lower court ruling.

Originally, Braidwood was suing Xavier Becerra, former President Joe Biden's HHS secretary. Now, the opposing party is Kennedy.

The oral arguments: Mitchell argued that the U.S. Preventive Services Task Force members are obviously principal officers who should be confirmed by the Senate.

"They cannot be inferior officers because their preventive care coverage mandates are neither directed nor supervised by the secretary of Health and Human Services or by anyone else who has been appointed as a principal officer," Mitchell said.

The governing statute "gives the task force alone the prerogative to impose preventive care coverage mandates on insurers, regardless of whether the secretary approves or disapproves a task force recommendation," he said. "Congress has chosen to create an independent task force and shield it from political pressure... And it is not even clear that Congress would have approved a regime in which politicians, rather than an independent task force, decide the preventive care that insurers must cover."

Mooppan maintained that the task force members are obviously inferior officers.

"They are subject to ample supervision by the secretary in issuing recommendations that bind the public," Mooppan said. "Most importantly, the secretary can remove task force members at will. His power to remove them flows from his power to appoint them acting through the director's authorities. And this court has repeatedly recognized that at-will removal power is a powerful tool for control. Moreover, the secretary can review task force recommendations and prevent them from taking effect."

Justice Brett Kavanaugh, one of the justices who likely would have to side with Mitchell and Braidwood for Braidwood to win, expressed skepticism about Mitchell's arguments about the independence of the task force members.

"I just don't see the indicators that this task force is more powerful than the secretary of HHS or the president," Kavanaugh said.

Amy Coney Barrett also expressed skepticism about Mitchell's arguments.

Mitchell interpreted the word "independent" in a "very maximalist way," Barrett told Mooppan. "You're taking a middle road."

The future: If the Supreme Court rules in Kennedy's favor, the current ACA preventive services package may survive, but it's possible that the arguments about Kennedy's control over the U.S. Preventive Services Task Force could make Kennedy more likely to fire task force members and overrule task force recommendations.