New Jersey failed to take advantage of the exception. Yet in 2011, New Jersey residents voted to amend the state constitution and allow the legislature to legalize sports betting, and it did so the next year. The N.C.A.A. and the four major professional sports leagues sued, arguing the law violated Paspa. A series of federal courts agreed, and the Supreme Court declined to hear the case.

The New Jersey legislature tried a new tactic in 2014, passing a law that partially repealed prohibitions on sports betting, believing that Paspa only prohibited the affirmative legalization of sports betting. Once again the N.C.A.A. and major professional sports leagues sued, and once again federal courts ruled against New Jersey.

But earlier this year, the Supreme Court surprised legal observers. Although the lower courts and the acting solicitor general for the United States, who asked the Supreme Court not to review the case, were all in agreement, the Supreme Court decided to hear the Christie administration’s challenge of Paspa anyway.

“It’s a very, very important case with respect to the division of authority in our system of government, between the federal government and state sovereign governments,” said Ted Olson, the attorney who will represent New Jersey in court on Monday.

Professional sports leagues, recognizing the ubiquity of illicit sports betting, have begun altering their longstanding stances against legalized sports betting, which they had feared might lead to game-fixing and other cheating. There is now an N.H.L. team playing in Las Vegas, and an N.F.L. team will soon join them. The N.B.A. is part of the group suing New Jersey, but in 2014 its commissioner, Adam Silver, wrote an Op-Ed article in The New York Times arguing for the legalization of sports betting.

“Sports betting should be brought out of the underground and into the sunlight where it can be appropriately monitored and regulated,” Silver wrote.

If the Supreme Court rules in favor of New Jersey, it could invalidate Paspa entirely and therefore allow every state to pass laws legalizing sports betting, or it could leave Paspa intact but rule that New Jersey’s law does not violate it. Olson said he does not believe such a narrow ruling is likely.