Graham said he spoke with McCain by phone on Sunday after the surgery in Arizona. He said McCain was doing much better and already itching to get back to Washington, though his doctors have told him he can't fly for a week while he recovers.
"He sounded like a different person. He clearly was a hurting guy," Graham said. "I think they relieved the pressure and he sounded like the old John McCain, dying to get back and talking about driving across the country. I said no."
Graham told CNN's Manu Raju that McCain had not been feeling well in the run-up to the surgery and was "getting forgetful."
"He'd been traveling a lot, we wrote it off that he was tired, but he was getting forgetful -- and you know he just wore himself out traveling all around the world," Graham said. "I'm glad they found out what I thought was the cause."
Later on Monday, Graham told CNN he wanted to retract that statement, saying that he did not mean to say that McCain was getting forgetful.
The Senate has delayed consideration of the health care bill this week with McCain's absence, as his vote at the moment would almost surely be needed for Republicans to get to 50 "yes" votes to pass the bill. McCain's office has said he'll be out at least a week.
Graham, a South Carolina Republican, spoke to McCain again by phone on the way to Monday evening's Senate vote -- the first that McCain was missing following the surgery .
Graham said it was a major surgery, but also has led a good outcome.
"He's got to heal up or he'll take a step backwards," Graham said. "I think they don't want him to fly for a week. But I think he would walk back if they'd let him. ... He's dying to get back and for the sake of his family I hope he doesn't have to stay there over a week."
In addition to the health care vote, McCain is supposed to lead debate on the annual National Defense Authorization Act on the Senate floor.
Graham said it wasn't clear yet if McCain would be back next week.
"I don't know. If it were up to him, he'd be on his way now," he said. "But he ... for once in his life, listen to his doctors. ... He's been hit pretty hard so it's going to take a while."