On Tuesday, Douglas N. Letter, a lawyer for the House of Representatives, was particularly insistent that Judge O’Connor had been wrong, telling the appeals panel that “the burden is on the other side to show Congress wanted this entire statute to be struck down.”

The arguments did reveal some tensions between the Republican states that brought the case, led by Texas, and Mr. Trump’s Justice Department. For example, a lawyer for Texas took issue with a puzzling new Justice Department position — revealed in a May brief — that the ruling should apply only in the 18 plaintiff states, not nationwide. The Republican states would need to evaluate if they had “been the victim of a bait and switch,” said the Texas lawyer, Kyle D. Hawkins.

In another wrinkle, August E. Flentje, a lawyer for the Justice Department, appeared reluctant to answer questions from Judge Elrod about how applying the ruling only to the plaintiff states would work. He was also vague about another new and surprising position the administration mentioned almost in passing in its May brief: that some pieces of the health law, though not its insurance provisions, should be preserved.

“A lot needs to get sorted out and it’s complicated,” Mr. Flentje replied.

Judge Elrod also asked how the federal government would respond if a stay issued by the lower court after Judge O’Connor’s decision was lifted and its order striking down the law took effect.

“We think it’s great the stay is in place,” Mr. Flentje said. “Those things don’t need to get sorted out until there’s a final ruling.”

Over all, though, the panel spent the most time on the question of whether the rest of the law should fall if Judge O’Connor was correct in scrapping the insurance mandate — and Judge Elrod and Judge Engelhardt, based on their questioning, seemed to firmly believe he was. Judge Engelhardt asked Mr. Letter, the House lawyer, why Congress could not remedy the situation by writing a new health law or set of laws.

“They could do this tomorrow,” Judge Engelhardt said, leading Mr. Letter to dryly point out that Mr. Trump would need to sign off on new laws, too.