Obama, who was in Wisconsin on Wednesday to give a speech on the economy, received a Packers jersey signed by Woodson with the message: "See you at the White House. Go Packers." Wisconsin Gov. Scott Walker and Green Bay Mayor James J. Schmitt greeted Obama at the airport and gave him the Woodson-autographed jersey, as well as another one with the president's name on the back.
"They're rubbing it in," Obama told reporters who traveled with him and witnessed the presentation.
Woodson said he voted for Obama and jokingly suggested that meant the President owed it to him to back the Packers.
Obama previously said he would attend the Feb. 6 Super Bowl in Arlington, Texas, if his favorite team made it. Instead, the Packers beat the Bears in Sunday's NFC Championship Game --- and presumably would make the Super Bowl winners' traditional visit to the White House if they beat the Pittsburgh Steelers for the title.
Blog: Presidential faux pas?
The sight of President Obama, perhaps the nation's most famous [Bears](/teams/chicagobears/profile?team=CHI) fan, holding up a [Packers](/teams/greenbaypackers/profile?team=GB) jersey might not sit well with some. What say you, Chicago? [**More...**](http://blogs.nfl.com/2011/01/26/how-does-this-sit-with-bears-fans/?module=HP_spotlight)
The president then predicted that his team will even the score next season.
"Sunday was a tough day for Bears fans," he said. "But even if it didn't go the way that I wanted, I'm glad to see that one of the greatest rivalries in sports is still there.
"And we will get you next year. I'm just letting you know."
The Associated Press contributed to this report.