"Josh plays with a lot of confidence," Wilks told reporters. "I think he gives us an opportunity to be able to be successful."
Rosen, the No. 10 overall pick, relieved Bradford late in the team's 16-14 loss to the Chicago Bears on Sunday. He got two chances in the final five minutes to move the Cardinals into range for a game-winning field goal but was unable to do so.
Starting from his own 25 with 4:31 left, Rosen moved Arizona to the Chicago 42 before being intercepted on fourth-and-5. The Cardinals got the ball back at their own 20 with 43 seconds left and no timeouts, and Rosen moved the ball near midfield, but he was sacked on the final play before he could get a Hail Mary to attempt off.
Wilks said he had decided to put Rosen in earlier -- after Bradford's third straight turnover with 11:23 remaining -- but the Bears ran nearly seven minutes off the clock before the Cardinals got the ball back. Still, Wilks wasn't worried about thrusting a rookie into the high-pressure, late-game situation.
"It looked like Josh was thrown in in the end, but he wasn't," Wilks said. "He can handle those types of situations. I think he handled it well. He went in, commanded the huddle, did a great job of moving the ball. We just, as an offense, in the end, didn't work well together."
Wilks wouldn't fully commit to Rosen starting the rest of the season, saying only, "Josh is our starter, and it's his job to lose." But the coach sounded optimistic about the rookie's ability to succeed.
"His demeanor is what you want at that position," Wilks said. "I don't think it's too big for him. ...
"I think you can sort of telling yesterday with some of his throws, and some of the accuracy. ... I thought he was pinpoint on all of them besides one."
Rosen thanked Bradford on Instagram later Monday, writing: "Since day 1, Sam has had my back and helped me become the best quarterback I could be. I cannot thank him enough for showing me how to be a professional in every sense of the word. He is a leader, a mentor, and a great person. He and Mike Glennon couldn't have been more supportive at a time that I thought might be a bit tense or awkward today. I couldn't be more thrilled to be in a QB room with two of the most selfless people I've ever been around as I start my career as a quarterback in the NFL. For that, I say thank you."
Bradford led Arizona to a 14-0 lead against Chicago while going 7 for 10 for 95 yards and two scores in the first half, but he threw interceptions on the first two drives of the second half before losing a fumble on the third. On the season, he is 50 of 80 for 400 yards, two touchdowns, and four interceptions, with the team scoring just 20 points in three games.
The Cardinals could have an incentive to move on from Bradford -- who signed a one-year, $20 million deal in the spring -- sooner than later. Bradford's contract includes a total of $5 million in roster bonuses, meaning he receives around $300,000 for every game in which he is active. The Cardinals paid Bradford a $10 million signing bonus.
Arizona has Glennon, also a free agent addition, third on the depth chart.