Mr. Baroni was sentenced to 18 months in prison in February and reported to a federal corrections facility in Pennsylvania in April, but he was released on bail after the Supreme Court agreed to hear the case in June.

Ms. Kelly was sentenced to 13 months but will remain free unless the Supreme Court rules against her.

The justices also struggled to decide a second legal question: whether the Port Authority had been defrauded of anything.

“The object of the deception was not to obtain property,” Justice Elena Kagan said, paraphrasing the words of the key federal law under which the defendants were prosecuted.

Chief Justice John G. Roberts Jr. echoed the point. “The object of the scheme was not to commandeer lanes on the bridge,” he said. “The object was to cause a traffic jam in Fort Lee. And if they could have done it some other way, they would have done it some other way.”

Mr. Roth, the lawyer for Ms. Kelly, drew a distinction between lies resulting in personal gain — expense account fraud, say — and ones told about the allocation of government resources.

“The federal property fraud statute is concerned with cheating the government out of its property rights,” Mr. Roth said. “And that’s just not what we have here. What we have here is an abuse of power, a political abuse of power.”

Allowing criminal prosecutions of such abuses under property fraud laws could have sweeping consequences, Ms. Kelly’s lawyers wrote in their Supreme Court brief. Under the government’s theory, they wrote, Commerce Secretary Wilbur Ross could be prosecuted for giving what the Supreme Court found in June was a contrived reason for trying to add a citizenship question to the 2020 census.