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Gibbs said the meeting between Obama and the conservative commentator should take place in a public setting, otherwise "nobody would believe it actually happened," CNN reported Tuesday.
The press secretary spoke one day after Obama was asked at an Indiana town hall meeting if he would accept Hannity's invitation to meet over a brew.
"I didn't know he had invited me for a beer, but I will take that under advisement. ... I'm always good for a beer," the president said.
Hannity said during his radio program later in the day that he was happy with the president's response to his offer.
"It seems like he's opened the door that he wants to meet with me," Hannity said. "Now if he does, I would go on your behalf."