"I'm usually accused of not being intense enough, right? Too relaxed?" he said, according to the network's account.
He seemed to blame Brewer for feeding the frenzy, saying that it is "always good publicity for a Republican if they're in an argument with me."
Brewer has done several interviews since she greeted Obama outside Phoenix Wednesday night. In one, she called the president "somewhat thin-skinned."
"This was really not a big deal," Obama told Sawyer. "She wanted to give me a letter, asking for a meeting. And I said, 'We'd be happy to meet.' "
He noted that according to her own account of a previous meeting between the two, she wasn't "fully satisfied."
White House officials seem more than eager to put the imbroglio behind them.
When Press Secretary Jay Carney was asked about it during a flight to Colorado, he shot back: "I'm glad you guys are focused on the important things," and he called it "political theater."