Hospital officials previously said Scalise would need multiple operations and weeks to recover after a bullet tore through his pelvis, fracturing bones, injuring internal organs and causing severe bleeding.
Sava said Scalise will require surgeries soon for abdominal and bone injuries, in addition to the two he has undergone to fix a bone in his leg broken by the bullet.
The source said investigators were not sure of the significance of the names and did not know if it was a list of people Hodgkinson was targeting. He arrived "in critical condition with an imminent risk of death", Dr. Jack Sava, director of trauma at the hospital, said Friday.
James T. Hodgkinson, was killed by police after the Wednesday shooting rampage.More news: Nadal wins; Muguruza crashes out of French Open
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The president said that because of the "tremendous pain and suffering he's now enduring. our country will perhaps become closer, more unified". "After he leaves the hospital he will require a period of healing and of rehabilitation".
The statement noted that there would be no further updates on Scalise's condition for the rest of the weekend.
Scalise, the third-ranking Republican in the House, underwent three surgeries, the latest one on Saturday. He died after officers in Scalise's security detail and local police fired at him.
Scalise was the most seriously injured of the four people Hodgkinson shot Wednesday morning. The annual GOP-Democrats baseball game raises money for charity. However, social media posts by the gunman earlier this year included profane comments about how much he disliked members of the Republican Party, which controls both houses of Congress. Hodgkinson has been identified as the suspect in the Wednesday, June 14, 2017, Washington D.C. shooting.