"What are we going to do, go back to kindergarten and before that and that's going to be part of this debate? It's silly," Axelrod said.
Axelrod has taken a shot at Romney over his dog story in the past, drawing a contrast between Obama and other pet owners by tweeting a photo of the president with his dog, Bo, riding inside the car.
How loving owners transport their dogs.bit.ly/xGeJuZ— David Axelrod (@davidaxelrod) January 30, 2012
In retaliation, top Romney adviser Eric Fehrnstrom recently tweeted a response to Axelrod's original tweet, adding the line: "In hindsight, a chilling photo."
Still, asked if Twitter is a new battlefront for campaigns in 2012, Axelrod dismissed the idea.
"I think Twitter can be a tool for getting information out that's valuable," he said. "I think it can be a positive thing."
Axelrod is well-known for responding via his Twitter feed to topics of the day, and for trading jabs with Fehrnstrom.