The long and short of it: she had no jurisdiction on consular security. That would be up to the state department. Rice is one of the candidates under consideration for the Secretary of State job.
Tomasky essentially makes the case that the Republicans, particularly McCain, went after Rice because of frustrations over the election and, perhaps most important in my view, failing to win the argument on foreign policy:
… most middle Americans recognize Benghazi for what it was—a terribly sad tragedy, but the kind of thing that, in a dangerous world, happens. And yes, many middle Americans would consider it a smudge on the administration’s security record, but most middle Americans also know that record is otherwise rather impressive. It seems to me someone just ran for president trying to argue otherwise, and he lost pretty handily.
And finally and maybe most of all, McCain and others are furious that the Republicans have lost their “natural” advantage on national-security issues. They are desperate to change that, and the quickest way to start doing so is to get Rice’s scalp.