I came across the phrase ‘tear a piece out of' Obama in the debate’ in the following statement in the article titled “Obama Math: Obama Math: 8.1 + 13,300 + 50 = 270” in New Yorker magazine (September 10):
“Of course, something could still happen to change the polling dynamics. Romney could tear a piece out of Obama in the debates; the tsunami of negative ads the Republicans are about to unleash could conceivably turn around some Obama-leaning states; there could be an “October surprise.” As of now, though, there is no sign of Romney getting the surge he needs.”
I guess ‘tear a piece out of” means to snatch an advantage out of, or take the lead to somebody (If my interpretation is wrong, please correct me), but I can’t find this phrase as an idiom in any of dictionaries at hand.
What does 'a piece' represent for? I mean 'a piece of' what? Is “tear a piece out of”somebody / something a popular idiom, or just a set of words?