At a press conference on Friday, the hospital treating the congressman said he has been sedated, but responded to family members.
Scalise, the third-ranking GOP leader in the House, "continues to show signs of improvement", MedStar Washington Hospital Center said in a statement released on behalf of his family.
President Trump and the first lady brought two bouquets of white flowers to the congressman who had undergone an emergency operation earlier that day after suffering a gunshot wound to the hip. "Dr. Jack Sava of MedStar Washington Hospital Center said it's a 'good possibility" that the Louisiana Republican will be able to return to work in his full capacity.
But Scalise can hope to make an "excellent recovery", his trauma surgeon said Friday.
The shooter was an IL man, James Hodgkinson, who had lashed out against President Donald Trump and Republicans over social media.
The bullet damaged blood vessels, bones, and internal organs, Sava said.
Scalise, Tyson Foods lobbyist Matt Mika, congressional aide Zach Barth and US Capitol Police officer Crystal Griner were shot during an attack on the Republican congressional baseball team as it practiced Wednesday morning.
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The shot fired at Scalise left perhaps hundreds of bullet fragments internally, many of which may never be removed because surgery might be more unsafe than leaving them in place, Sava said.
One source told CBS News the note is not considered an "assassination list", but it is clear Hodgkinson had a group of people he was focused on recently.
Doctors "fully expect him to walk", Sava said, "and hopefully run".
"It's been much more hard than people even thought at the time", Trump told reporters at the White House on Thursday, adding that he also had visited a wounded Capitol Police officer at the hospital. After discharge he will need a period of healing and rehabilitation.
Doctors say representative Steve Scalise remains in critical condition, but they are encouraged by the progress he has made.
The person did not disclose the names, but said those listed had been briefed.
Bailey was spotted Friday back in the Capitol building, on crutches and out of uniform, accepting congratulations from fellow officers.