On Monday night, general manager Tom Heckert said he fully expects Weeden to win the competition. McCoy, entering his third season in the NFL, has been promised the chance to keep the job.
"I can only go by what they tell me," McCoy said Tuesday (May 22) after a 90-minute session to open OTAs. "This is the card that has been dealt. I'm working as hard as I can. I thought today went great. One of my favorite quotes by the Navy SEALS is, 'The only easy day was yesterday.'
"As a quarterback you have to be able to thrive amid difficulties. I don't want to make this me vs. Seneca (Wallace) or me vs. Brandon. I want to make this about what is best for our team. I don't want there to be any distractions about 'Am I the quarterback or is Brandon the quarterback?' Hopefully the best person will play."
Weeden said essentially the same thing Tuesday, as he has since the night he was drafted on April 26.
Coach Pat Shurmur juggled the lineups in OTAs so at times Weeden was with the first group and at others McCoy was with the starters.
"I think they did some good things," Shurmur said. "I think they practiced fast and they made some good throws, although there were some errors in there. We'll go in there and correct them when we see the tape."
What a difference for McCoy. He was 2-6 as a starter in 2010, lost his last three starts, combined for one touchdown pass and six interceptions in losses to the Ravens and Steelers in the final two games and was still named the starter for 2011 even before Shurmur was hired as head coach.
The 2011 season ended with McCoy on the sideline for the last three games recovering from a concussion. One of the last things team president Mike Holmgren told him as players headed home for the offseason was to expect competition in 2012.
The rumbling grew louder in March when the Browns offered the Rams three first-round draft picks for the second pick. They would have used it on quarterback Robert Griffin III. When the Redskins outbid Cleveland for the Griffin pick the Browns used the 22nd pick on Weeden.
"You can imagine a little bit (what I was thinking), I guess," McCoy said. "But for me, I've read what was said. I heard what was said. I guess my attitude is I've always just wanted to let everyone say what they needed to say. I understand the idea, and if it's a fair competition, then that's all you can ask for.
"I mentioned it earlier. I don't want this to be a situation where it's me vs. him or him vs. me. Let's make it about the Cleveland Browns being a great football team next year. And if that's the case, I'm all in."
McCoy was 4-9 as a starter last season. He said he feels no after-effects from the concussion.