Greeley was wearing a Barack Obama baseball cap when he fell over the weekend, fracturing his skull and suffering bleeding on the brain.
As the cab began to pull away, the 80-year-old priest fell to the ground and hit his head, fracturing his skull.
He was taken to Advocate Lutheran General Hospital in Park Ridge, where he remained in critical condition as of 4:45 a.m. Monday, according to a hospital nursing supervisor, who said his condition had not changed.
Earlier, his niece Laura Durkin said he was in critical but "very stable" condition and doctors were pleased with Greeley's progress from Friday to Saturday.
Greeley, who was wearing a Barack Obama baseball cap when he fell, suffered bleeding on the brain.
Doctors installed a monitor in his skull to gauge pressure on his brain, said his friend and attorney Terry Goggin. CT scans are also being used to monitor his injuries.
Greeley was transferred from the hospital's emergency room to its surgical intensive care unit, where he remained sedated Saturday. Other than the implantation of the pressure monitor, he has not had surgery, Goggin said.
The outspoken Catholic scholar has written more than 50 novels, including some best sellers. He writes a regular column for the Chicago Sun-Times. His books have been translated into 12 languages.
He lectured Friday at the Religious Education Association conference in Rosemont. "Greeley was very generous and very funny," association executive secretary W. Alan Smith said.
After his speech, Greeley, who lives in the John Hancock Center, hailed a cab for the short trip to the CTA station on River Road.
"He's a Chicago guy -- 'take the L,' " said Goggin.
Although he was swollen and bruised, Greeley's color looked good Saturday morning and he was "resting comfortably" after a restless night, Goggin said.
"You know, he's a fighter and a tough guy," Goggin said. "He's got everything they want in a patient. All the signs are very positive."