The left tackle told the team's website: "All the confidence in the world. [McCown] came in and did his thing. He spread the ball around, he got us in good position, and we had a chance to win the game.
"You always want your guy out there. You know how competitive of a person [Cutler] is. You just feel sorry that he has to deal with it.
"But at the end of the day, Josh has been in the league for a long time. He's played a lot of games. He has a lot of experience. So we're excited about the opportunity."
McCown completed 204 passing yards during the team's 45-41 loss to the Washington Redskins last weekend.