Browns coach Pat Shurmur said McCoy was checked by the team's medical staff before he was told to get rest. Flushed from the pocket, McCoy was laid out on the helmet-to-helmet hit by Harrison, who was suspended for one game. McCoy, who has started Cleveland's first 13 games, has not practiced this week and Wallace has taken every snap with the Browns starting offense.
The Browns have endured a whirlwind of controversy since their decision to re-insert McCoy back into the game against the Steelers. On Wednesday, team president Mike Holmgren revealed that the Browns trainers did not check the quarterback for a concussion during the two plays he was on the sideline and did not see the hit which injured McCoy.
As he addressed Cleveland media, Holmgren defended the Browns decision-making process during the game, stating McCoy didn't show any concussion-like symptoms until well after the game.
Shurmur hasn't completely ruled McCoy out, but said if McCoy doesn't practice it's logical Wallace will start against the Cardinals.
"Seneca's been taking all the snaps," Shurmur said. "Two plus two."
Shurmur also said that Thaddeus Lewis can handle the role of the team's No. 2 quarterback and could execute the Browns' playbook in Sunday's game if necessary.
Shurmur said tight end Benjamin Watson, who has had three concussions this season, visited a specialist on Wednesday. Shurmur said it's possible Watson's season could be over.
"We're hoping to get him back)," Shurmur said. "There could be a chance he doesn't."
Strong safety T.J. Ward (foot) will have to take step back in workload Thursday after practicing Wednesday, Shurmur said.
The Associated Press contributed to this report.