The 82-year-old Williams has taken "a real step forward," Jeffrey Borer, his New York cardiologist, told The Boston Globe.
"In terms of the current phase of his recovery, he's already made it," Borer said Thursday. "His heart is doing what it has to do."
"This is the period when we could expect non-cardiac problems to become important difficulties, and they haven't been yet. That doesn't mean they won't become so."
Williams, the former Red Sox great and last major leaguer to hit .400, had surgery Jan. 16 in New York to repair a valve in his heart.
"We're on the road to success here," Williams' son, John Henry Williams, said. "It's another challenge, and he's great at overcoming challenges."
A brain specialist Wednesday night also confirmed hopeful signs of brain function that doctors and the family had observed.
"The neurologist called him by his name," Borer said, "and noted a response. Then he called him by another name, and he didn't respond."
The next critical step is for Williams to begin talking, which Borer said "is just a matter of time - he attempts to speak now."
David Adams, associate chief of surgery at Brigham and Women's Hospital, said Williams' chances of survival "have improved a lot."
"He has made it beyond a lot of important hurdles," said Adams, a heart specialist.
John Henry Williams said support has been flowing in from across the country, including a phone call from President Bush.
"I feel like I'm a switchboard," said the son, who has also fielded calls from Dom DiMaggio, who played alongside Williams a half-century ago, and former Dodgers manager Tommy Lasorda.
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