Sava added that Scalise "was as critical as you can be when he came in" after a single rifle shot traversed his body from his left hip through internal organs to the other hip as witnesses said he was fielding ground balls.
Investigators say he shot House Rep. Steve Scalise before he was killed by police who had been guarding the congressman.
Organizers made a decision to go on with the game on Wednesday, hours after the shooting. It appears that Scalise, his Republican colleagues and others, who were practicing for a charity baseball game, were targeted by a man - who died from his own wounds - who disagreed with Republicans' positions.
Officials said Hodgkinson was carrying notes on which he had written the names of some Republican lawmakers.
Scalise's surgeon said on Friday he can hope to make an "excellent recovery", even though when he arrived at the hospital he was at imminent risk of death.
Members of the US Congress took part in the traditional Republicans vs Democrats baseball game on Thursday, with many wearing hats to honour Steve Scalise, the congressman who was critically wounded by a gunman as his team practised a day before.
"After he leaves the hospital, he will require a period of healing and of rehabilitation".
Doctors "fully expect him to walk", Sava said, "and hopefully run". "I feel a lot more optimistic than I did two, three days ago".
"I want to take a moment to send our thoughts, love, and prayers to Congressman Steve Scalise and his entire family".
In that bad crime, the country also witnessed the incredible heroism of the Capitol Police, he said, adding that Special Agent Crystal Griner - who he also met during his visit to the hospital - raced into gunfire, along with Special Agent David Bailey.
The mood at the Capitol remained somber Thursday, as members learned more about Scalise's condition and signed giant "get well" posters for him and others injured. On Friday, Bailey was spotted back in the Capitol building, on crutches and out of uniform, accepting congratulations from fellow officers.
David Bailey, a Capitol Hill police officer who was part of Mr Scalise's security detail and helped bring down the shooter, was also injured in the incident but had recovered enough to throw the game's ceremonial first pitch.