I like Jessica. She's very talented, but she's been far from perfect during the competition. (That Gloria Estefan number comes to mind.) The only American Idol contestant I can recall who seemed incapable of fucking up was Melinda Doolittle, who had a flawlessness in her performances that, not surprisingly, led to her being shown the door at Top 3. She came across as too polished, too professional to be "America's" discovery.
I really think most of the backlash that comes her way are those threatened by her inability to fuck up!
I think Jessica's biggest obstacle is the judges treating her like she already has the thing in the bag. Folks who like her (and would be inclined to pick up the phone for her) become complacent and those who are rooting for other contestants vote even harder for them in protest.
American Idol is as much a personality contest as it is a talent one. Jessica's personality is not particularly noteworthy one way or the other. In this contest, that's a problem.