"Who is going to take his spot? I don't know yet," Guillen said. "Whoever is throwing the ball better.
"It's one guy we're going to miss, especially in this series. The best hitters they have in the lineup are lefties, but you got to deal with what you deal with, and hopefully [Thornton] comes back for at least one day while we're here."
Octavio Dotel could be Guillen's choice if the White Sox need a big strikeout, but as Guillen pointed out, it's tough to fan the likes of Mauer or Morneau. Scott Linebrink, the team's primary right-handed setup man, would seem to be the top option against lefties, possessing the best changeup and split leading up to Bobby Jenks.
Linebrink knows that Thornton will be briefly missed, but he also knows that Mauer or Morneau can connect against lefties as well as righties.
"They are just good hitters, and you have to do your job and do what you can to get them out," Linebrink said. "Certainly, Thornton has been the logical choice for lefties because he's been so good against them.
"But I don't think it's so much righty-lefty, as much as missing a good quality arm at the end of the game. We all have to take up the slack right now, and we are up to the challenge."
While the White Sox try to figure out their late-inning setup for the next few days, they still have a decision to make on Clayton Richard. The left-hander figured to return to the bullpen after Sunday night's start, giving the White Sox a second left-hander with Thornton, but his stretch of two earned runs allowed over the past 16 innings has given Guillen pause about the move out of the rotation.
As of Monday, the White Sox rotation is set through Friday, with Mark Buehrle, Bartolo Colon, Jose Contreras and Gavin Floyd getting the next four starts. Richard could go Saturday against the Yankees, giving Buehrle a couple of extra days of rest with Monday's off-day, or Richard could be skipped for the interim while the White Sox judge Colon's effort.
"We're in the pennant race, but the good deal for the future is to keep him out there," said Guillen of Richard. "We got to see what's best for the club."