SANTA CLARA – Quarterback Alex Smith gave a thumbs up to his sore middle finger Wednesday.

"It's doing fine," said Smith, who did some light tossing Monday and Tuesday. "The more you move it around, keep it going, it'll get better as the week goes on."

Smith injured the finger on his throwing hand late in the 49ers' 45-3 win over the Bills on Sunday when he was hit by defensive end Mario Williams and braced himself as he hit the ground. Smith played two more snaps – both runs by Smith – but didn't throw another pass before he was taken out of the game.

He was diagnosed with a sprain after having X-rays taken immediately afterward.

Smith went through pre-practice warm-ups Wednesday without a bandage on the finger. While he was listed on the team's injury report, he was a full participant in the afternoon session.

Smith said he didn't know whether he would need to protect the finger Sunday against the Giants.

"At this point, maybe a little tape for support," he said. "Like I said, it's one of those things where everyone's kind of had them. The more you move them, keep them going, the better they'll be."

Hail to the Chief – The first thing President Barack Obama said upon meeting Vernon Davis and Smith at a fundraising dinner Monday night in San Francisco had to do with the 49ers' game against the Chicago Bears on Nov. 19.

"You know you're playing (the Bears) soon, right?" Davis quoted Obama as saying.

Davis met Obama, a Bears fan, in February at another San Francisco fundraiser at which the tight end spoke. After that speech, Obama took the podium and invited Davis to join the Bears, a comment that received good-natured boos from the crowd. Davis brought his 5-year-old son Jianni to the dinner Monday. Smith was with his wife, Elizabeth.

Smith didn't need Davis to get him into the event. His younger sister Mackenzie works for the chair of the Democratic National Committee, Debbie Wasserman Schultz.

"Very cool. Huge honor," Smith said of meeting the president. "He talked ball the whole time. He was down to earth. Knew what was going on with us, talked a lot about us, the game on Sunday, our schedule, knew we were playing the Bears. So it was cool."

Davis also attended the White House Correspondents Dinner earlier this year in his native Washington, D.C., and he has been open on social media about his support for Obama. Not surprisingly, he said that support has attracted criticism from the anti-Obama crowd, but he said it doesn't bother him.

"When I put a picture up, a picture of me and Alex, we got some comments on Instagram. People were talking crazy," he said. "You get a lot of reaction."

Injuries – Running back Brandon Jacobs (knee) and punter Andy Lee (hand) were the only two other 49ers on the injury report. Both practiced in full.

The Giants listed 13 players on their injury report, including starting wide receiver Hakeem Nicks (foot, knee), who didn't practice.

© Copyright The Sacramento Bee. All rights reserved.

• Read more articles by Matthew Barrows

Order Reprint