Dr. Gail Roboz, speaking on GMA, said Roberts, in characteristic fighting fashion, had already sent her an email message saying she "wanted to go home!"
But, the oncologist, who called Roberts, 51, "a powerhouse," noted that the next 7-10 days were crucial for the injected stem cells, donated by Roberts's sister Sally-Ann, to grow properly, ridding her of the rare blood disorder, myelodysplastic syndrome.
"It's not instant," Roboz told show host George Stephanopoulos. "Rebuilding ... takes weeks to months," with a goal of leaving the hospital in about 30 days.
As the doctor explained, "We have to roll with the punches over the next few days because, don't forget, her systems are down and Sally-Ann's aren't up yet so we're in that in-between zone of watching very carefully. We are wanting every day to be a good day, but we are ready for some bumps in the road.”
Roberts, who had thanked supporters via video message, was surrounded by TV colleagues and friends Diane Sawyer and Sam Champion on Thursday for the transplant.
After a blessing of the harvested stem cells and prayer, her fave tunes, including "Ain't No Mountain High Enough," were played during the brief procedure.