Hamilton injured his groin late in the third quarter of Friday night's game against the Los Angeles Clippers and sat out Sunday night's game against the Memphis Grizzlies. Watson strained his left elbow in Sunday night's contest and was seen at the Berto Center on Monday wearing a sling on his arm.
"Rip did a little more today so he's feeling a little bit better," Thibodeau said after Monday's practice. "C.J. is at the doctor's right now so we still don't know on him."
Thibodeau said that Hamilton would be a game-time decision Tuesday night while he admitted that Watson would probably be out for an undetermined amount of time.
"That would be my guess," he said of Watson. "It's a sprain. (Athletic trainer) Fred (Tedeschi) saw him this morning and the swelling's not too bad. But he's visiting the doctor now. It will be day to day basically. We'll go from there."
Watson's injury was hard for Bulls point guard Derrick Rose to stomach.
"It was messed up," Rose said. "It was definitely messed up. I thought it was worse than what it was. But we have other people that can come in and replace him for a little bit of time before he gets back. It's definitely going to hurt us, but there's no excuses. We still got to go out there and play these games. We know that he'll be back shortly."
Thibodeau noted that the team has confidence that Bulls backup point guard John Lucas III could come in and take over Watson's minutes.
"He's been around for a while," Thibodeau said. "He played two years in Houston. He's played overseas. We have a lot of confidence in him. He can shoot the ball, he can run the team so that's the way it is. One guy gets hurt, the next man has to step up."
As for Hamilton, he is taking a wait and see approach. He said he didn't do much during practice except shoot a little more.
"We'll see," Hamilton said. "I think we're day by day right now. It's a little better today than it was (Sunday) and the day before so that's a good sign."
Initially, Hamilton didn't even think his injury was that bad, although he admitted he has dealt with groin injuries before during his time with the Detroit Pistons.
"I thought it was just something minor," Hamilton said. "Something that maybe (I could) ice and had a day off the next day and maybe it would a lot better, but it wasn't."
Nick Friedell covers the Bulls for ESPNChicago.com.