Opting to remain amateur so he could play in the Olympics, McInnis spent the majority of the 1991–92 season with the United States men's national ice hockey team where he recorded 34 points in 54 games. At the 1992 Albertville Olympics, McInnis led the American team in scoring with five goals and two assists in eight games as the United States finished fourth in the tournament. McInnis turned professional following the tournament as he joined the Islanders for 15 games late in the 1991–92 NHL season where he scored three goals and five assists. He made his NHL debut on March 3, 1992, against the Montreal Canadiens and scored his first goal on March 8 against goaltender Tom Draper of the Buffalo Sabres.