(CBS) President Barack Obama hosted the Super Bowl Champion Green Bay Packers at the White House Friday and suggested the team trade star quarterback Aaron Rodgers to the Chicago Bears.

Obama is a longtime Bears fan and admitted it was hard for him to welcome the rival Packers into the White House.

“This hurts a little bit,” the president said. “This is a hard thing for a Bears fan to do. It doesn’t hurt as much as the NFC Championship Game hurt, but it still hurts. You guys coming to my house to rub it in. What are you going to do? Go to Ditka’s house next?”

LISTEN: President Obama welcomes the Green Bay Packers to the White House

The Packers beat the Bears 21-14 at Soldier Field last January to advance to the Super Bowl.

“Enjoy it while it lasts because Bears fans have two dates circled on our calendars: Sept. 25 and Sunday night football on Christmas Day,” Obama warned the Packers. “If you guys are on a roll by then, just keep in mind that there’s only one person here who can ground all planes in and out of Green Bay if he has to.”

Packers cornerback Charles Woodson then presented the president with public shares to the team. The Packers are the only publicly owned team in professional sports. The shares made Obama one of over 112,000 people who own a portion of the Packers.

“If I’m a part owner … I think we should initiate a trade to send Rodgers down to the Bears,” he said.

Of course, those comments aren’t exactly supportive of current Bears quarterback Jay Cutler and it didn’t take long for the White House to realize this. White House spokesman Adam Abrams sent CBSChicago.com the following statement to clarify why Obama would welcome Rodgers to the Bears:

“The President understands the value of having a reliable backup QB – and would make it more likely that he could greet the Bears at a similar ceremony at the White House next year.”

Aaron Rodgers backing up Jay Cutler? Not likely.