Jim McGrath said no plan for the former first lady's discharge has yet been made, the Los Angeles Times reported.
"She's still doing great, still in great spirits. We have not heard any plans for discharge just yet -- we're still in a wait-and-see mode," McGrath told the Times. "She's keen to get home to her dogs and her husband -- and not in that order," he said. "When I talk to her, she sounds like she's 100 percent."
Bush, 88, was admitted Monday to Methodist Hospital at Texas Medical Center. Her husband, former President George H.W. Bush, has been a regular visitor, McGrath said.
President Obama released a get-well message Wednesday: "Michelle and I send our best wishes to Mrs. Bush for a speedy recovery. Barbara is blessed to have both a loving, supportive family by her side and a vibrant spirit that we hope will have her feeling better soon. I know I speak for Americans everywhere when I say that our thoughts and prayers are with Barbara and her family on this New Year's Day."
President Bill Clinton sent a tweet to his predecessor's Twitter account: "I'll be rooting for Barbara Bush's full recovery while she's rooting for Baylor today. All my best to her and George H.W. Bush."
Baylor lost in the Fiesta Bowl to Central Florida 52-42.
McGrath said the former first lady appreciates the "good wishes."
"She doesn't want anybody to make a fuss -- that's Barbara Bush," he said.