I don't think we know anything on Secretary of State other than that the only two people seriously considered and vetted were Kerry and Rice. I think it also safe to say that where Kerry, per several articles, asked his supporters to not lobby on his behalf, Rice actively had her proponents do so. I suspect that this difference had no impact - Obama knew what each brought to the job and it was his choice.
I do think that one thing that the media never suggested was that perhaps putting Rice in the position of being on those 5 talk shows was to some degree a "test". A more political person, such as Hillary Clinton or John Kerry, could have navigated the hearings by staying within what was known. (If you think this unfair, I remind you that there have been 10s of things the media called "tests" for the 2004 Presidential nominee with a far higher political and even international profile.)
I think that Obama's defense of Rice was something that ANY high level official should get against unfair charges. Each time, he took pains to say both that this would not stop him AND tha he had not made his choice.
I have MORE problems with the WP using the criticism to say that IF Obama did not then nominate her, the person they had blatantly favored for the nomination, it sent a message that he was weak.