Although I wouldn't say he's been completely consistent with his character over that time. The degree to which he emphasizes being champion has definitely changed between giving up a shot at the title to help Zack Ryder and his mini-feud with JBL during the whole JBL/HBK storyline in 2008/2009. Really Cena still has had some weird fluctuations over the years where he'll spend a week or two acting like a hateful, selfish bastard before returning to his usual routine.
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Mistake you're making - overlooking the fact that we might not want to be saved.