Why is she so popular? All I know about her is she survived breast cancer, replaced a corrupt governor (she was actually part of his administration), and signed civil unions into law.
I live in the state, so I've been watching her closely for the past 1-1/2 years that she's been governor.
Part of it is that she isn't John Rowland. He was pretty popular up until 2003, but lost his popularity when his lying became clear. She came in like a breath of fresh air, and projected enough distance from him not to get caught up in his scandals.
Part of it is her personality. She has a very pleasing personality, and appears to be open to various points of view.
She gives the conservatives (or what pass for conservatives in Connecticut) just enough to keep them from revolting, while appearing open to more liberal viewpoints.
Interestingly enough, I got a fundraising letter from her recently, and she didn't mention a word about civil unions. She successfully presented it in such a manner that she is credited with settling the issue without allowing gay marriage, and that's enough for her supporters.
She refused to commute the death sentence of Michael Ross earlier this year, another popular position. She also said that if the state legislature tried to repeal the death penalty, she would veto it. The attempted repeal failed by a large margin.
Part of her popularity is that she didn't really have to make very hard choices in her budget. State revenues are up, and incumbent governors are usually popular when that is the case. And her strongest potential opponent -- Richard Blumenthal -- has chickened out of a run.
There is also a feeling even among many Democrats that the Democratic party should not control both the legislative and executive branches.