There is more than one type of heel. And this list is not comprehensive, just the three I've seen the most.
The most famous type of heel is the cowardly heel. This is the heel that talks tough but won't get in the ring and back his words up and he ends up winning the title through cheating (or cashing in MITB contracts) and retaining it through disqualifications. There have been several incarnations of this heel as it is the easiest type of heel to portray and is usually mixed with the second type. Popular cowardly heels: Daniel Bryan, Christian, Edge
The second type is the cheating heel. The cheating heel is good enough as a wrestler to "win" titles, but prefers to get his victories through cheating, getting disqualified (so long as it doesn't cost him the title), and other types of "unfair" ways, including sometimes just getting the lucky break. The cheating heel is often cowardly as well as the two styles are a natural mix. Popular cheating heels: Ric Flair, Kurt Angle in the early part of his WWE career, HHH in most of his heel runs, ADR
The third type is the dominant heel. The dominant heel is usually a power wrestler who just comes out and destroys faces. There is no arguing with the dominant heel as he is boastful and enough of a bad-@$$ to back up his boasts. Dominant heels tend to look down on other heels as well as the faces. The problem with the dominant heel is that these are heels that some segments of the fandom will cheer for, because they are easy to respect (part of the draw of pro wrestling is, after all, the physical nature of the show). The cheers typically will eventually turn most dominant heels face. The problem with that is most pro wrestling companies tend to force their faces to conform to a set of rules that kill the dominant heel's heat (see: Punk, CM - 2011, post-MITB). Popular dominant heels: Brock Lesnar, Mark Henry in his "World's Strongest Man" gimmick, HHH in his later heel runs, Sheamus in his "Celtic Warrior" gimmick (which they went away from because Sheamus was getting cheers despite his heel status), (as before mentioned) CM Punk during the run-up to his WWE Championship challenge at Money in the Bank (sadly leading to the afore-mentioned loss of heat after his face turn when WWE tried to force him into becoming Cena Lite)
The reason I mention these is to point out that a Cena heel turn would not necessarily detract from the people who already support him. He would be a dominant heel, which fits his conviction that he wouldn't change his persona to fit a wrestling "character". He just wouldn't talk as much about "hustle, loyalty, respect"; he would just go out and destroy whoever he was against. It would just require him being booked against faces rather than heels and still being booked to win.
Having said that, I agree with Crayo that making him go through a full recognized heel turn is not the smart option. All that is required is that he be booked a little differently but continue to be dominant. He would also continue to bring out that edgier, more aggressive side of his personality, effectively changing his character to a dominant heel character without going through a "heel turn", thus keeping him the casual "Face of the WWE" and continuing to allow the Make-a-Wish kids to ask for him as the most-requested Make-a-Wish request ever, but allow the character to develop, which, in the end, will be good for everybody.
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