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“If I was put in this position, there’s no question I would recuse myself,” he said. “But I suspect the White House and others don’t want her to recuse herself because they have a huge amount of politics and everything else riding on this case and having it come out the right way.”

The choice to recuse is entirely up to each justice, though public pressure can raise the profile of the decision.

In the case of Justice Thomas, several dozen congressional Democrats signed a letter this year saying that his wife’s stated opposition to the health care law and her work for the Heritage Foundation should disqualify her husband.

“Given these facts, there is a strong conflict between the Thomas household’s financial gain through your spouse’s activities and your role as an associate justice of the United States Supreme Court,” the lawmakers said. “We urge you to recuse yourself from this case. If the U.S. Supreme Court’s decision is to be viewed as legitimate by the American people, this is the only correct path.”

The justices did not recuse themselves in the court’s decision Monday to hear the case.

Mr. Sample said that “hints” that there won’t be a recusal later, but that it’s not definitive because a justice can decide any time between now and when a ruling is issued in the case.

“I’m not a betting man, but, I guess I’d say I’d be very surprised if any of the justices recuse in this case,” Mr. Sample said. “It is going to be a major issue, but it’s going to be a major issue outside the U.S. Supreme Court building.”