It would be a daunting task for anyone making his first argument before the Supreme Court.

As the lawyer representing a group of Colorado voters seeking to block former President Donald J. Trump from the ballot, Jason Murray, 38, stood before a skeptical majority in a high-stakes argument that could shape the course of the presidential election.

He was also appearing before two of his former bosses: Justices Elena Kagan and Neil M. Gorsuch.

After finishing Harvard Law School, he clerked for Justice Gorsuch, then a judge on the U.S. Court of Appeals for the 10th Circuit, and later spent a year working for Justice Kagan, finishing in 2014.

The pair are often on opposing sides in ideologically charged cases on issues like abortion, voting rights and affirmative action. But both Justice Kagan, a liberal nominated by President Barack Obama, and Justice Gorsuch, a Trump appointee who has helped shift the court to the right, seemed troubled by the implications of the Colorado Supreme Court’s decision to bar Mr. Trump from the primary ballot. Each pummeled Mr. Murray with a punishing barrage of questions.

Justice Kagan pushed Mr. Murray on the implications of allowing Colorado to ban Mr. Trump, questioning what would happen if the state at the heart of the case were instead a swing state like Michigan or Wisconsin.

“Maybe put most boldly, I think that the question you have to confront is why a single state should decide who gets to be president of the United States,” Justice Kagan said. “That seems quite extraordinary, doesn’t it?”

Mr. Murray responded that it was “not unusual that questions of national importance come up through different states.”