President Obama won't pick a winner in next Sunday's Super Bowl now that his Chicago Bears have been eliminated, he said Thursday.

Obama said he's staying neutral in the championship matchup between the Pittsburgh Steelers and the Green Bay Packers, set for Feb. 6 in Dallas.

The president noted that he'd been deluged with ribbing by Packers fans while he was in Wisconsin on Wednesday. They beat the Bears this past Sunday, despite Obama's prediction otherwise.

Obama's poor pick in that game was cause for motivation for Pro Bowl cornerback Charles Woodson, who said publicly that the team would come to see Obama at the White House -- once they'd won the Super Bowl. Obama was presented with an autographed Woodson jersey on Wednedsay.

"Woodson's a great player, and one of my favorite players in the NFL," the president said in a live chat on YouTube. "But I've got to stay absolutely neutral on this, and may the best team win."

Despite his close ties to the Rooney family, which owns the Steelers, Obama said he wouldn't pick a winner. The head of the family, Dan Rooney, is the president's ambassador to Ireland.