Federal Reserve Chairman Ben Bernanke’s term ends in January, and it looks like he’s ready to hang up his Fed fedora. Now there’s an unusual, very public battle to influence President Obama’s decision on who should replace Bernanke. A Fed food fight between two camps:  One supporting Fed Vice Chair Janet Yellen, the other backing former Treasury Secretary and White House economic adviser Larry Summers.

“I think it’s unprecedented and I think, frankly, it’s a little silly,” says Alice Rivlin, a former Fed vice chair.  She says there aren’t major policy differences between Yellen and Summers.  So you have to blame politics.

“There is a lot of polarization between the parties and a lot of sense that this is a big moment in the economy so everybody is kind of getting their oar in,” Rivlin says.

A group of Democratic senators sent a letter to President Obama urging him to support Yellen. Newspapers are weighing in with editorials, some highly critical of Summers and praising Yellen, who would be the first female Fed chair. Women’s rights advocates are lobbying for Yellen to make history.

“This would be viewed as really a landmark breaking of the glass ceiling in central banking,” says  Ken Kuttner, a Fed economist for 15 years.

Some Yellen backers are zeroing in on controversial comments Summers made about women, which helped cost him his job as Harvard president.  Other Summers critics point to his ties to Wall Street — though that’s a plus for his supporters. Summers’ strong personality  is also fueling the public feuding.

 “As they would say down in Texas, he’s a hard dog to keep under the porch,” says Bob McTeer, a former president of the Dallas Fed. 

McTeer says all of the bickering could make room for a dark horse.

“If they kill each other off,” he says. “If they have a circular firing squad,  yes, that’s a conceivable outcome.”

 But we’ll have to wait a while for any outcome. The White House says it won’t nominate Bernanke’s replacement until this fall.