And it's deep enough that one of the team's most vocal Twitter users is vowing to quit using the service.
Rodgers didn't directly address the way his injured teammates chose to express their disappointment about potentially being left out of the Super Bowl team photo. But, without naming anyone, he said Saturday that some of the team's 16 injured players chose not to stay in town and rehabilitate.
"I'll say this, I was on IR back in 2006 and I chose to stick around and finish out the season with my guys and be here every game. Some of those guys didn't," Rodgers said. "Some of the guys who were injured, they still are part of this team, but they didn't choose to stick around."
Barnett, who hasn't played since Week 4 because of a wrist injury, fired back at Rodgers on Twitter.
"Looks like people have something to say about where some people choose to do there rehab," Barnett wrote. "Try rehabing with 16 others then 53 more. Doubt you get the full attention needed.. It's easy to speak about others when you are not in their position.. Talk about 'union' ha."
Barnett, who later erased those tweets, added: "Goodbye twitter... It was fun while it lasted.. But we need to focus on important things.
"I was never trying to be a distration," Barnett tweeted. "I am packer have been one for 8 going on 9 years. ... I love this team this city.. All I wanted to be is included as a teammate nothing more.. Looks like it has back fired on me.. I guess that was asking too much... Sorry if I offended anyone.. That was not my intention."
Tight end Jermichael Finley, who hasn't played since Week 5 because of a knee injury, also weighed in Saturday night.
"For my followers that want to know why im rehabbing in AZ, bc I get the top of the line training," Finley wrote on Twitter. " ... Think before y'all speak. Fans listen, I love u all, and have been working my tail off 5 hrs a day since I have arrived in Arizona. I love the packers.
"Everyone in the NFL knows that this is a business and if I don't take care of my body to be Best player than I can be, then I won't even be around to win a Super Bowl in the future. I'm a packer for life, AROD is my guy!"
McCarthy said Thursday the players made a "poor decision" when they complained about it in public, but that it was no big deal to change the timing of the photo.
At the time, McCarthy said the attention paid to the issue was a "total overreaction." He completed his media availability Saturday before Rodgers made his comments.
McCarthy also said Thursday that he was advised to expect such distractions while preparing his team for the Super Bowl.
"We'll be as organized as we possibly can," McCarthy said. "Something is going to be screwed up. I've been told that by a number of coaches. So you have to be able to let it roll off your back, and somebody else is going to get their feelings hurt. We're going to continue to make sure that we do everything that's in the best interests of getting our football team ready to win this game."
The Associated Press contributed to this report.