Judge Sotomayor’s colleagues on the United States Court of Appeals for the Second Circuit say her tough and direct questioning reflects engagement and, sometimes, an effort to persuade her colleagues. Those qualities, coupled with a gregarious personality, they said, make her a powerful force behind the scenes, where she has used her mastery of the cases to change minds, improve opinions and forge consensus.

Those skills, some observers say, could make her an able politician on the Supreme Court and allow her to serve as an intellectual counterweight to Justice Antonin Scalia, a conservative who is known for his acerbic questioning.

“In some ways she could match, well, the other New Yorker on the court, Justice Scalia,” said Douglas Kmiec, a law professor at Pepperdine University. “He expects people to give back as good as he gives, and I expect that when Justice Sotomayor is on the court, his wish will be fulfilled.”

Both colleagues and lawyers who have argued before her agree that her style is assertive.