"Out of respect to the owner, I'm not commenting," said Walker, who went back to working with Jim Thome and Carlos Quentin following his brief statement.
Walker has been close with White Sox chairman Jerry Reinsdorf since his playing days 25 years ago. It was Reinsdorf who told MLB.com at the end of the disappointing 2007 campaign that anyone who knew anything about the game wasn't questioning the job done by the team's hitting coach.
Reading between the lines of Walker's no-comment, it's clear that Walker was less than pleased with Guillen's postgame outburst. The highly-professional hitting coach did not display his displeasure outwardly, however.
Guillen and Walker had not spoken as of Tuesday afternoon. But Guillen had plenty to say about the status of Walker's job. It wasn't quite the resounding vote of confidence issued by Guillen in the past.
"Well, the players are gonna dictate," said Guillen. "When I have to fire one of my coaches, I do it right away. I did in the past. I'm the manager of the ballclub, and he's the hitting coach.
"That's baseball. His job is fine right now. It's fine right now. But ... how long? ... I believe in his philosophy, I believe in how hard he works, but make it work. Make it work. It would be more fun. More fun for everyone."
As has been proven over the past 1 1/2 seasons, that request is easier said than done. Guillen did explain the inclusion of Walker's name Sunday, pointing out how it was the offense being criticized and Walker is the leader of the offense.
If it was a pitching issue, Don Cooper would have been called out. If the infield was the problem, then bench coach Joey Cora's name was going to be out there.
"How many times have I protected Greg Walker?" said Guillen. "That's our job. Who am I gonna blame? Me? I blame myself, too.
"I just begged the players a couple days ago to start hitting for him because I know how much this kills him. He's our hitting coach. I'm protecting my coaches the most I can, as long as they work, as long as they do what they're supposed to do, and as long as they're here every day with the players to help them."
With Guillen having control of the coaches' hiring and firing, he will ultimately make the call on Walker and any other member of his staff. General manager Ken Williams and Guillen have said numerous times before that they don't make changes solely to make someone a scapegoat for a team's struggles.
And when Guillen was asked Tuesday if Walker was doing his job, the White Sox manager responded that Walker was doing that and more. Even so, Walker could become the unfortunate odd man out if the offense doesn't turn around soon.
"I told Walker: 'Relax. Get out of the cage. Don't even talk to those people,'" Guillen said. "That hurts. That kills Greg Walker right now. I think [Monday] was the worst day off he ever had in his career, yesterday."