Taylor's talent was evident from the start of training camp. Reports came out of the Giants training compound of the exploits of the new . Taylor's teammates took to calling him Superman and joked that his locker should be replaced with a phone booth. Phil Simms, the team's quarterback, said, "on the pass rush, he's an animal. He's either going to run around you or over you. With his quickness, he's full speed after two steps." Taylor made his NFL exhibition debut on August 8, 1981, recording 2 sacks in the Giants' 23–7 win over the Chicago Bears. Before the season word spread around the league about Taylor. Years after facing him in an exhibition game, Pittsburgh Steelers Quarterback Terry Bradshaw recalled, "dang-near killed me, I just kept saying, 'Who is this guy?' He kept coming from my blind side and just ripped my ribs to pieces."