The 18-year-old NeSmith opened with even-par 70. He was 1-under for the tournament through 10 holes today. But a missed fairway at No. 11 led to double bogey. Then, he bogeyed No. 13.
NeSmith finished with 71 to finish two rounds at 1-over-par 141. The cut line was 139.
Jimmy Walker shot 62 to top the leaderboard at 12-under.
Defending champion Webb Simpson was a stroke back after 63, and first-round leader Carl Pettersson, Tim Clark, Sergio Garcia and rookie Harris English were 10-under. Pettersson had 68, Clark shot 67, Garcia 63 and English 64.
Tim Herron matched the tournament record with 61, but was still seven strokes back.
Play was halted for 1 hour, 17 minutes late in the day when a system of thunderstorms passed through the central North Carolina Triad.