Beckham said his wrist did not feel much better when he woke up Wednesday, but it did improve after getting treatment.
He still has not swung a bat since leaving Tuesday night's game in the third inning after feeling pain while fouling off a pitch in his first at-bat during Chicago's 8-7 loss to the Washington Nationals.
"I think tomorrow will be the big test. If I wake up and it feels better, I think it'll be fine. If not, we'll probably have to do an MRI or something," Beckham said Wednesday. "I'm actually happy about the way it's felt since I've gotten to the field and done some work to it. So that's a positive thing and hopefully tomorrow it'll be that much better."
In another lineup change Wednesday, Adam Dunn returned to action, getting his first start of the season in left field. Dunn, who usually is Chicago's designated hitter, sat Tuesday for the opener of the interleague series with no DH at Nationals Park.
Beckham was in the lineup at second base for the season's first seven games, and is batting .316.
"It's a little frustrating, but it's a minor setback as of right now," he said. "I expect to be back out there in a couple days. And hopefully feel fine, 100 percent, and keep going with where I started -- I feel good about that -- and help this team."
He said he's never dealt with a wrist problem.
"I'd like to be back on the field as soon as possible. But obviously ... I don't want to rush this and make it a worse thing for the entire season. As much as I want to get back out there, that's the smarter play," Beckham said. "And that's probably what we'll end up doing -- we'll be a little more cautious than you would be toward the end of the season."
Manager Robin Ventura agreed with Beckham that Thursday will be a key test for the second baseman.
As for whether a stint on the disabled list because of the nerve irritation in Beckham's wrist is possible, Ventura said: "In the next couple of days, you'll know. You'll know probably by tomorrow if it's heading that direction. You kind of prepare for it, but you hope it doesn't happen."
White Sox pitching coach Don Cooper is still hospitalized with a stomach illness. Ventura is not sure whether Cooper will be able to travel with the team for its series that begins Friday at the Cleveland Indians. ... Chicago LHP John Danks threw six innings in an extended spring training game, reaching 89 mph, Ventura said.