Dr. Greg Stewart, Tulane University's director of sports medicine, said Walker remained in stable condition in the intensive care until of St. Francis Hospital in Tulsa, Okla. Physicians there will plan to do surgery on Walker in the coming days, he said.
"These kind of injuries take 24, 48, sometimes 72 hours to full declare themselves," Stewart said. "We don't know what the long-term implications and outcomes are going to be."
Stewart said he was with Walker on the field, in the ambulance and at the hospital on Saturday. He said Walker was put into a cervical collar and couldn't see much of what was happening, so Stewart explained what was going on. Walker was talking with doctors as he was being treated, Stewart said.
Walker's parents had travelled to Oklahoma to be with their son, and they were "doing as well as can be expected," Stewart said.
"They're like the rest of us — hopeful and prayerful."
Stewart was back in New Orleans on Sunday, as were Walker's teammates. He said Tulane's athletic director and the football team's trainer remained in Oklahoma with Walker.
Walker's injury occurred on the final play of the first half, hours after Tulane opened the Conference USA portion of its schedule against Tulsa. Tulsa was leading 35-3 and facing a fourth-and-2 with the ball at the 33-yard line on Saturday when the Golden Hurricane called timeout. Tulane then called timeout.
When play resumed, Tulsa quarterback Cody Green tossed a short pass to Willie Carter, who caught it at about the 28, and turned upfield. He was tackled around the 17-yard line, with defensive tackle Julius Warmsley and Walker sandwiching him and apparently smashing their helmets together.
Medical personnel from both teams tended to Walker as he lay on the field. FOX Sports reported a hush went over the crowd at H.A. Chapman Stadium as Walker was attended to, and that several coaches were in tears as he was taken away in an ambulance. Spectators bowed their heads as someone on the field led the stadium in prayer.
Dr. Buddy Savoie said during a postgame news conference that Walker never completely lost consciousness and was breathing on his own.
"He was stable when we transported him," Savoie said. "I do not think, based on the information we have, his life was ever in danger."
Walker is a senior majoring in cell and molecular biology. His brother, Raynard, told The Associated Press on Saturday that their mother was watching the game on television when her son was injured.
Tulane head coach Curtis Johnson said after the 45-10 loss that while Walker was on the field, Johnson told Walker that he was praying for him and that help was on the way.
He said the mood among players was sombre and called the day his most difficult ever.
"It was tremendous that they finished the game, as I thought about just saying 'Hey look, let's not do anything else. Let's just get on the road and go.'"
Associated Press writer Emily Wagster Pettus contributed to this report from Jackson, Miss.